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C₂×#20255111 #27091524

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 69 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)(54,55)(56,65)(57,61)(58,67)(59,62)(60,68)(63,66)(64,69);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(51,53)(54,57,59,58)(55,61,62,67)(56,64,66,68)(60,65,69,63);(54,56,59,66)(55,60,62,69)(57,64,58,68)(61,65,67,63);(50,51)(52,53)(54,55,59,62)(56,63,66,65)(57,61,58,67)(60,68,69,64);(48,49)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1044814);