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C₂×#4150 #66282

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1620);