Finite Group Databasebeta

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C₂×#20276888 #27538825

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

526 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)(58,70)(60,73)(61,77)(62,75)(63,79)(65,82)(66,85)(67,84)(68,86)(69,74)(71,81)(72,80)(76,83)(78,87);(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)(56,58,69,78,62,71,60,61)(57,63,76,66,67,80,65,68)(59,70,74,87,75,81,73,77)(64,79,83,85,84,72,82,86);(56,57,62,67)(58,68,71,66)(59,72)(60,76,69,65)(61,63,78,80)(64,81)(70,84)(73,86)(74,85)(75,79)(77,82)(83,87);(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, 324301);