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C₂×#31241 #7503869

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

Aliases

Subgroups

2460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411065);