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C₂×#12583 #492898

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

Aliases

Subgroups

2570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400094);