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C₂×#20251851 #27079751

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 81 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(50,54,55,67)(51,58,59,73)(52,62,63,79)(53,64,65,66)(56,69,60,75)(57,70,71,72)(61,76,77,78)(68,80,74,81);(50,53,55,65)(51,57,59,71)(52,61,63,77)(54,66,67,64)(56,68,60,74)(58,72,73,70)(62,78,79,76)(69,81,75,80);(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)(50,52)(51,56)(53,61)(54,62)(55,63)(57,68)(58,69)(59,60)(64,76)(65,77)(66,78)(67,79)(70,80)(71,74)(72,81)(73,75);(50,51)(52,60,63,56)(53,57)(54,58)(55,59)(61,74,77,68)(62,75,79,69)(64,70)(65,71)(66,72)(67,73)(76,81,78,80);(48,49)

Conjugacy classes & character table

1646 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033041);