Finite Group Databasebeta

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C₂×#20276793 #27538475

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

686 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)(57,65)(58,70)(60,74)(61,76)(62,77)(63,75)(64,73)(66,81)(67,83)(68,84)(69,82)(71,85)(72,80)(78,87)(79,86);(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)(56,58,62,71,63,72,60,61)(57,64,68,78,69,79,66,67)(59,70,77,85,75,80,74,76)(65,73,84,87,82,86,81,83);(56,57,63,69)(58,67,72,78)(59,73,75,86)(60,68,62,66)(61,64,71,79)(65,80,82,70)(74,87,77,83)(76,84,85,81);(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, 323951);