Finite Group Databasebeta

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C₂×#20276496 #27537118

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 91 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)(60,63,66,65)(61,68,70,80)(62,73,76,75)(64,77,79,72)(67,81,82,85)(69,78,83,91)(71,84,86,90)(74,88,89,87);(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)(60,62,72,87,65,75,79,89,66,76,77,88,63,73,64,74)(61,67,78,84,68,81,83,86,70,82,91,90,80,85,69,71);(56,57,58,59)(60,61)(62,71)(63,68)(64,78)(65,80)(66,70)(67,74)(69,72)(73,84)(75,90)(76,86)(77,83)(79,91)(81,88)(82,89)(85,87);(54,55)

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 322594);