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C₂×#6554 #90615

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

94 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1377);