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C₂×#5526 #85722

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 25 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18298);