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C₂×#20254465 #27087655

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 89 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(51,55)(54,56)(60,69)(64,78)(68,83)(70,85)(77,88)(79,86)(82,89)(84,87);(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)(52,57)(54,56)(58,61,63,73)(59,65,67,80)(60,68,69,83)(62,75,76,72)(64,77,78,88)(66,81,74,71)(70,87,85,84)(79,89,86,82);(50,52,53,57)(51,54,55,56)(58,60)(59,64)(61,68)(62,70)(63,69)(65,77)(66,79)(67,78)(71,82)(72,84)(73,83)(74,86)(75,87)(76,85)(80,88)(81,89);(50,51)(52,56)(53,55)(54,57)(58,59,63,67)(60,64,69,78)(61,71,73,81)(62,74,76,66)(65,75,80,72)(68,82,83,89)(70,86,85,79)(77,87,88,84);(48,49)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1040945);