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C₂×#4133 #66259

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

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

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1597);