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C₂×#59847 #7665867

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

Aliases

Subgroups

8506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573063);