Finite Group Databasebeta

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C₂×#20276402 #27536925

• 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)(58,67)(62,78)(66,80)(68,71)(69,74)(77,85)(79,87)(84,86);(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)(57,62)(59,71)(60,74)(61,67)(63,80)(64,79)(65,78)(66,70)(68,73)(69,76)(72,77)(75,85)(81,86)(82,84)(83,87);(56,57,60,64,61,65,76,83)(58,66,69,84,67,80,74,86)(59,70,72,82,73,63,75,81)(62,77,79,71,78,85,87,68);(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, 322401);