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C₂×#20748 #6370995

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

Aliases

Subgroups

4560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6278191);