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C₂×#20255168 #27092482

• 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:

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

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1045772);