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C₂×#21065 #6371643

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

Aliases

Subgroups

4018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278839);