Finite Group Databasebeta

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C₂×#20257985 #27123650

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

6458 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)(51,57)(55,58)(56,63)(62,64);(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)(52,60)(55,58)(59,65)(62,64)(66,69,70,77)(67,73,72,76)(68,75,74,80)(71,78,79,81);(50,53,54,61)(51,56,57,63)(52,59,60,65)(55,62,58,64)(67,72)(68,74)(73,76)(75,80);(50,52,54,60)(51,55,57,58)(53,59,61,65)(56,62,63,64)(66,68)(67,71)(69,75)(70,74)(72,79)(73,78)(76,81)(77,80);(50,51)(52,58)(53,56)(54,57)(55,60)(59,64)(61,63)(62,65)(66,67,70,72)(68,71,74,79)(69,76,77,73)(75,81,80,78);(48,49)

Conjugacy classes & character table

1226 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076940);