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C₂×#12567 #492873

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

Aliases

Subgroups

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400069);