Finite Group Databasebeta

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C₂×#5735 #86216

• 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)(6,8,9,12)(7,11,10,13)(15,21)(19,27)(20,29)(26,28);(6,7)(8,11)(9,10)(12,13)(14,17,18,25)(15,20,21,29)(16,22,23,24)(19,26,27,28);(8,12)(11,13)(14,16,18,23)(15,19,21,27)(17,24,25,22)(20,28,29,26);(4,5)(7,10)(8,12)(14,15)(16,19)(17,20)(18,21)(22,26)(23,27)(24,28)(25,29);(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, 18792);