Finite Group Databasebeta

?

← Prev (#27538649) Next (#27538651) →

C₂×#20276836 #27538650

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

678 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)(56,58)(57,65)(59,70)(60,74)(61,69)(62,71)(63,75)(64,79)(66,83)(67,81)(68,82)(72,85)(73,84)(76,87)(77,80)(78,86);(56,57,64,77,61,67,73,78,62,68,72,76,60,66,59,63)(58,65,79,80,69,81,84,86,71,82,85,87,74,83,70,75);(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)(57,63)(58,69)(59,64)(60,61)(65,80)(66,77)(67,76)(68,78)(70,84)(71,74)(72,73)(75,81)(82,87)(83,86);(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, 324126);