Finite Group Databasebeta

?

← Prev (#27538460) Next (#27538462) →

C₂×#20276781 #27538461

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

706 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)(57,64)(58,68)(60,72)(61,78)(62,74)(63,79)(65,80)(66,83)(67,82)(69,85)(70,86)(71,77)(73,76)(75,81)(84,87);(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)(56,58,60,69,62,70,76,61)(57,63,65,66,67,77,75,84)(59,68,72,85,74,86,73,78)(64,79,80,83,82,71,81,87);(56,57)(58,66)(59,71)(60,75)(61,77)(62,67)(63,69)(64,68)(65,76)(70,84)(72,83)(73,87)(74,79)(78,80)(81,85)(82,86);(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, 323937);