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C₂×#20254041 #27086116

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1842 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)(50,52,53,56)(51,55,54,57)(60,69)(64,77)(68,83)(70,82)(76,88)(78,85)(81,89)(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)(58,61,72,79,63,74,62,73)(59,65,75,86,67,80,66,71)(60,68,82,87,69,83,70,84)(64,76,85,89,77,88,78,81);(51,54)(55,57)(58,60,63,69)(59,64,67,77)(61,68,74,83)(62,70,72,82)(65,76,80,88)(66,78,75,85)(71,81,86,89)(73,84,79,87);(50,51)(52,55)(53,54)(56,57)(58,59,63,67)(60,64,69,77)(61,71,74,86)(62,75,72,66)(65,79,80,73)(68,81,83,89)(70,85,82,78)(76,87,88,84);(48,49)

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1039406);