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C₂×#45448 #7702067

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

Aliases

Subgroups

9740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7609263);