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C₂×#20276847 #27538663

• 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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 324139);