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A054396
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Numbers m such that there are precisely 4 groups of order m.
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23
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28, 30, 44, 63, 66, 70, 76, 92, 102, 117, 124, 130, 138, 154, 170, 172, 174, 182, 188, 190, 230, 236, 238, 246, 266, 268, 275, 279, 282, 284, 286, 290, 315, 316, 318, 322, 332, 354, 370, 374, 387, 412, 418, 426, 428, 430, 434, 442, 465, 470, 494, 495, 498
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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For m = 28, the 4 groups of order 8 are C7 : C4, C28, D28, C14 x C2 and for m = 30 the 4 groups of order 30 are C5 x S3, C3 x D10, D30, C30 where C, D mean cyclic, dihedral groups of the stated order and S is the symmetric group of the stated degree. The symbols x and : mean direct and semidirect products respectively. - Muniru A Asiru, Nov 04 2017
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MATHEMATICA
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PROG
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CROSSREFS
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Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), this sequence (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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