Finite Group Databasebeta

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C₂×#20276388 #27536883

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1230 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)(56,59,61,72)(57,63,65,80)(58,67,69,70)(60,71,75,87)(62,76,77,78)(64,79,73,86)(66,82,81,84)(68,83,74,85);(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)(56,58,61,69)(57,62,65,77)(59,70,72,67)(60,74,75,68)(63,78,80,76)(64,81,73,66)(71,83,87,85)(79,82,86,84);(56,57)(58,66,69,81)(59,63)(60,73,75,64)(61,65)(62,68)(67,82,70,84)(71,86,87,79)(72,80)(74,77)(76,83)(78,85);(54,55)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 322359);