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C₂×#20276461 #27537050

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 322526);