Finite Group Databasebeta

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C₂×#20282868 #27590458

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 79 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)(58,62)(60,63)(72,75,76,73)(74,77,78,79);(57,61)(60,63)(66,70)(68,71)(72,74,76,78)(73,77,75,79);(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)(56,58)(57,60)(59,62)(61,63)(64,66)(65,68)(67,70)(69,71)(73,75)(74,78);(56,57)(58,60)(59,61)(62,63)(64,65,67,69)(66,68,70,71)(72,73,76,75)(74,77,78,79);(54,55)

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 375934);