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C₂×#35808 #7629193

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

Aliases

Subgroups

9842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536389);