Finite Group Databasebeta

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C₂×#20276183 #27413038

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 198514);