Finite Group Databasebeta

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C₄×#1010 #85822

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 23 points:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18398);