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C₂×Dic₁₆₉₆ #27305142

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 183 points:

(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(56,58,63,75)(57,64,69,98)(59,77,82,130)(60,84,87,147)(61,89,91,151)(62,93,90,74)(65,100,103,164)(66,105,107,172)(67,109,110,174)(68,111,92,97)(70,112,115,76)(71,99,94,79)(72,104,120,78)(73,108,122,85)(80,137,139,183)(81,141,138,129)(83,95,144,157)(86,149,132,146)(88,96,150,159)(101,166,167,180)(102,168,152,163)(106,173,142,171)(113,177,178,136)(114,126,123,140)(116,165,154,182)(117,135,153,162)(118,175,179,124)(119,133,145,169)(121,176,181,125)(127,161,158,131)(128,160,155,134)(143,170,148,156);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(56,57,63,69)(58,70,75,115)(59,76,82,112)(60,83,87,144)(61,88,91,150)(62,92,90,68)(64,94,98,71)(65,99,103,79)(66,104,107,78)(67,108,110,85)(72,118,120,179)(73,121,122,181)(74,123,93,114)(77,105,130,172)(80,136,139,177)(81,140,138,126)(84,100,147,164)(86,148,132,143)(89,113,151,178)(95,155,157,128)(96,158,159,127)(97,117,111,153)(101,165,167,182)(102,135,152,162)(106,133,142,169)(109,154,174,116)(119,180,145,166)(124,161,175,131)(125,160,176,134)(129,173,141,171)(137,170,183,156)(146,168,149,163);(54,55)

Conjugacy classes & character table

3398 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90618);