Finite Group Databasebeta

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C₂×#5651 #86002

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 29 points:

(1,2)(3,4,5)(6,8)(7,11)(9,12)(10,13)(14,18)(15,21)(16,23)(17,25)(19,26)(20,27)(22,29)(24,28);(6,7)(8,11)(9,10)(12,13)(14,17,19,16)(15,20,22,24)(18,25,26,23)(21,27,29,28);(7,10)(11,13)(14,16)(15,20)(17,19)(18,25)(21,28)(22,24)(23,26)(27,29);(4,5)(8,12)(11,13)(14,15,19,22)(16,20,17,24)(18,21,26,29)(23,27,25,28);(1,2)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18578);