Finite Group Databasebeta

?

← Prev (#27413009) Next (#27413011) →

C₂×#20276165 #27413010

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 87 points:

(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)(56,59,60,71,61,72,74,85)(57,63,64,77,65,78,80,87)(58,67,68,83,69,70,73,84)(62,75,66,81,76,86,79,82);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,58)(57,62)(59,70)(60,73)(61,69)(63,75)(64,79)(65,76)(66,80)(67,72)(68,74)(71,83)(77,82)(78,86)(81,87)(84,85);(56,57)(58,66,69,79)(59,63)(60,64)(61,65)(62,68,76,73)(67,82,70,81)(71,77)(72,78)(74,80)(75,84,86,83)(85,87);(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, 198486);