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C₂×#10396 #239401

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

Aliases

Subgroups

1766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 146597);