Finite Group Databasebeta

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C₂×#20276603 #27537522

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

646 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)(56,59,61,60,62,73,78,75)(57,64,66,72,67,82,76,65)(58,69,77,74,70,86,71,87)(63,79,84,85,80,68,81,83);(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)(57,63)(59,69)(60,74)(61,77)(62,70)(64,79)(65,83)(66,84)(67,80)(68,82)(71,78)(72,85)(73,86)(75,87)(76,81);(56,57)(58,68,70,79)(59,72)(60,64)(61,76)(62,67)(63,69,80,86)(65,73)(66,78)(71,83,77,85)(74,84,87,81)(75,82);(54,55)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 322998);