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C₂²×#15689399 #27083666

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 83 points:

(1,2)(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)(52,55)(53,60)(54,65)(56,70)(57,72)(58,71)(59,73)(61,69)(62,77)(63,76)(64,78)(66,80)(67,82)(68,81)(74,83)(75,79);(52,54,57,67,58,68,56,66)(53,59,62,74,63,75,61,64)(55,65,72,82,71,81,70,80)(60,73,77,83,76,79,69,78);(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)(52,53,58,63)(54,64,68,74)(55,69,71,77)(56,62,57,61)(59,67,75,66)(60,72,76,70)(65,79,81,73)(78,82,83,80);(50,51);(48,49)

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1036956);