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C₂×#23886 #6437595

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

Aliases

Subgroups

6285 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344791);