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C₂×#23911 #6437434

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

Aliases

Subgroups

6274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344630);