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C₂×#20276486 #27537102

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

658 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)(56,59,62,61)(57,64,66,76)(58,68,70,71)(60,72,75,74)(63,77,78,87)(65,73,79,86)(67,80,81,85)(69,82,83,84);(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)(56,58,60,69,61,71,74,84,62,70,75,83,59,68,72,82)(57,63,65,67,64,77,73,80,66,78,79,81,76,87,86,85);(56,57)(58,67,70,81)(59,64)(60,73)(61,76)(62,66)(63,69,78,83)(65,74)(68,80,71,85)(72,79)(75,86)(77,82,87,84);(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, 322578);