Finite Group Databasebeta

?

← Prev (#27414071) Next (#27414073) →

C₂×#20276298 #27414072

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

662 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)(56,59,60,74,61,75,62,76)(57,64,65,81,66,72,77,86)(58,68,69,83,71,84,70,73)(63,78,67,80,79,87,82,85);(56,58,62,69,61,71,60,70)(57,63,77,67,66,79,65,82)(59,73,76,68,75,83,74,84)(64,80,86,87,72,85,81,78);(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)(48,49)(50,51)(52,53)(56,57,60,65,61,66,62,77)(58,67,69,79,71,82,70,63)(59,72,74,86,75,64,76,81)(68,80,83,87,84,85,73,78);(54,55)

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 199548);