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C₂×#22427 #6379052

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

Aliases

Subgroups

5598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286248);