Finite Group Databasebeta

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C₂×#20276531 #27537219

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 87 points:

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

Conjugacy classes & character table

2144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 322695);