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C₂×#12695 #493364

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

Aliases

Subgroups

3790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 400560);