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C₂×#30535 #7501034

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

Aliases

Subgroups

3664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7408230);