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C₂×#20273344 #27352116

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 87 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)(56,59,61,60)(57,63,64,65)(58,67,68,69)(62,70,66,71)(73,78)(77,85)(79,86)(80,87);(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)(57,62)(59,67)(60,69)(61,68)(63,70)(64,66)(65,71)(72,74)(73,77)(75,83)(76,82)(78,85)(79,87)(80,86)(81,84);(56,57,60,65,61,64,59,63)(58,66,67,71,68,62,69,70)(72,73)(74,80,82,87)(75,79)(76,78)(77,81,85,83)(84,86);(54,55)

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 137592);