Finite Group Databasebeta

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C₂×#20276921 #27538868

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 95 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,58,59,62)(57,61,60,63)(65,71)(67,78)(68,79)(70,82)(72,73)(74,87)(75,89)(76,90)(80,88)(81,86)(83,84)(85,94)(91,95)(92,93);(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)(57,60)(61,63)(64,66,69,77)(65,70,74,85)(67,75,80,91)(68,76,79,90)(71,82,87,94)(72,83,86,93)(73,84,81,92)(78,89,88,95);(56,57)(58,61)(59,60)(62,63)(64,65,69,74)(66,70,77,85)(67,71,80,87)(68,81,79,73)(72,88,86,78)(75,82,91,94)(76,92,90,84)(83,95,93,89);(54,55)

Conjugacy classes & character table

1202 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 324344);