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C₂²×#870 #85669

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 23 points:

(1,2)(3,4)(5,6,7)(8,10,11,14)(9,13,12,15)(17,21)(20,23);(9,12)(13,15)(16,18,19,22)(17,20,21,23);(6,7)(8,9,11,12)(10,13,14,15)(16,17)(18,20)(19,21)(22,23);(3,4);(1,2)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18245);