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C₂×#59148 #7666204

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

Aliases

Subgroups

9278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573400);