Finite Group Databasebeta

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C₂²×#812 #83723

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16299);