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C₂×#15227 #608548

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

Aliases

Subgroups

11806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 515744);