Finite Group Databasebeta

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C₂×#20260575 #27144040

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 163 points:

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

Conjugacy classes & character table

1094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 6814);