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C₂×#13411 #499083

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

Aliases

Subgroups

1274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406279);