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C₂×#13381 #498995

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

Aliases

Subgroups

1380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(8,9)(11,12)(13,16)(14,17)(15,23)(18,22)(19,21)(20,24)(25,26);(3,4)(5,6)(7,8)(9,10)(12,16)(17,24)(18,25)(19,23);(4,6)(7,9,10,8)(12,17)(14,22)(15,21)(16,24)(18,19)(20,26)(23,25)

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, 406191);