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C₂×#33728 #7623212

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

(1,2);(3,4,6,8)(5,9,10,7)(11,12)(13,22)(14,19)(15,29)(16,31)(17,21)(18,26)(20,24)(23,35)(25,36)(27,41)(28,34)(30,42)(32,38)(33,40)(37,39);(3,5,6,10)(4,7,8,9)(13,23)(18,32)(22,35)(25,27)(26,38)(33,37)(36,41)(39,40);(11,13,24,39,16,27,30,38,17,23,28,40,14,25,15,26)(12,18,29,36,19,33,34,35,21,32,42,41,31,37,20,22);(11,14,17,16)(12,19,21,31)(13,25,23,27)(15,28,30,24)(18,33,32,37)(20,29,34,42)(22,36,35,41)(26,40,38,39)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530408);