Finite Group Databasebeta

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C₂×#5701 #86105

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2)(3,4,5)(6,9)(7,11)(8,12)(10,13)(14,17,18,26)(15,20,21,24)(16,23,22,25)(19,28,27,29);(6,8,10,7)(9,12,13,11)(16,22)(19,27)(23,25)(28,29);(9,13)(11,12)(14,16,18,22)(15,19,21,27)(17,25,26,23)(20,29,24,28);(4,5)(6,7,10,8)(9,11,13,12)(14,15,18,21)(16,19,22,27)(17,24,26,20)(23,29,25,28);(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, 18681);