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C₂×#20253103 #27083668

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 81 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)(50,54,56,55)(51,59,61,60)(52,64,66,65)(53,68,69,70)(57,72,73,62)(58,74,75,67)(63,78,79,80)(71,81,77,76);(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)(50,53)(51,58)(52,63)(54,68)(55,70)(56,69)(57,71)(59,74)(60,67)(61,75)(62,76)(64,78)(65,80)(66,79)(72,81)(73,77);(50,52,54,64,56,66,55,65)(51,57,60,62,61,73,59,72)(53,63,68,78,69,79,70,80)(58,71,67,76,75,77,74,81);(50,51)(52,62)(53,67)(54,59)(55,60)(56,61)(57,64)(58,68)(63,77)(65,73)(66,72)(69,74)(70,75)(71,79)(76,78)(80,81);(48,49)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1036958);