Finite Group Databasebeta

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C₂×#4823 #78979

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11555);