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C₂×#20275252 #27386090

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1694 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)(56,59,62,75)(57,64,66,72)(58,68,70,84)(60,74,61,73)(63,77,78,86)(65,80,76,79)(67,81,82,87)(69,85,71,83);(56,58)(57,63,66,78)(59,68)(60,69)(61,71)(62,70)(64,77,72,86)(65,67,76,82)(73,83)(74,85)(75,84)(79,87,80,81);(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)(56,57,61,65,62,66,60,76)(58,67,71,78,70,82,69,63)(59,72,74,80,75,64,73,79)(68,81,85,77,84,87,83,86);(54,55)

Conjugacy classes & character table

1826 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 171566);