Finite Group Databasebeta

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C₂×#20276409 #27536934

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1198 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)(56,59,62,60)(57,64,66,73)(58,68,71,69)(61,72,76,74)(63,67,79,80)(65,81,83,82)(70,85,75,77)(78,84,87,86);(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)(56,58,62,71)(57,63,66,79)(59,69,60,68)(61,75,76,70)(64,80,73,67)(65,78,83,87)(72,85,74,77)(81,86,82,84);(56,57,61,65,62,66,76,83)(58,67,70,84,71,80,75,86)(59,64,72,81,60,73,74,82)(63,77,78,68,79,85,87,69);(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, 322410);