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C₂×#43111 #7667373

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

Aliases

Subgroups

9992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7574569);