Finite Group Databasebeta

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C₂×#20276658 #27537864

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 91 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)(47,48)(49,50)(51,52)(57,59)(60,63,66,65)(61,68,70,80)(62,72,74,81)(64,75,79,78)(67,83,85,84)(69,76,87,90)(71,88,89,86)(73,77,82,91);(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)(48,49)(50,51)(52,53)(60,62)(61,67)(63,72)(64,77)(65,81)(66,74)(68,83)(69,86)(70,85)(71,76)(73,78)(75,82)(79,91)(80,84)(87,88)(89,90);(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)(48,49)(50,51)(52,53)(56,57)(58,59)(60,61,66,70)(62,71,74,89)(63,68,65,80)(64,76,79,90)(67,82,85,73)(69,75,87,78)(72,88,81,86)(77,83,91,84);(54,55)

Conjugacy classes & character table

1202 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 323340);