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C₄×#15689937 #27080518

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2658 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)(55,66)(59,73)(63,77)(67,79)(71,82)(74,80)(76,83)(78,81);(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)(52,55)(53,59)(54,63)(56,67)(57,66)(58,71)(60,74)(61,73)(62,76)(64,78)(65,77)(68,80)(69,81)(70,79)(72,82)(75,83);(52,54,57,65)(53,58,61,72)(55,63,66,77)(56,69,70,64)(59,71,73,82)(60,75,68,62)(67,81,79,78)(74,83,80,76);(52,53,57,61)(54,62,65,75)(55,59,66,73)(56,68,70,60)(58,69,72,64)(63,76,77,83)(67,80,79,74)(71,81,82,78);(48,49,50,51)

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033808);