Finite Group Databasebeta

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C₂×#20258035 #27123775

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

6554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 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)(66,70,71,69)(67,75,74,73)(68,77,78,79)(72,80,76,81);(50,53,54,61)(51,57,56,60)(52,59,58,64)(55,62,63,65)(67,74)(68,78)(73,75)(77,79);(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)(51,56)(52,58)(57,60)(59,64)(66,69,71,70)(67,73,74,75)(68,77,78,79)(72,80,76,81);(50,52)(51,55)(53,59)(54,58)(56,63)(57,62)(60,65)(61,64)(66,68)(67,72)(69,79)(70,77)(71,78)(73,81)(74,76)(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)(50,51,54,56)(52,55,58,63)(53,60,61,57)(59,65,64,62)(66,67,71,74)(68,76,78,72)(69,75,70,73)(77,80,79,81);(48,49)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1077065);