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C₂×#20603 #6370717

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

Aliases

Subgroups

17206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277913);