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C₂×#5648 #85994

• 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:

(1,2)(3,4,5)(6,7)(8,9)(10,14,15,13)(11,17,18,22)(12,19,20,21)(16,24,25,23);(1,2)(7,9)(10,13)(11,17)(12,19)(14,15)(16,23)(18,22)(20,21)(24,25);(10,12)(11,16)(13,21)(14,19)(15,20)(17,24)(18,25)(22,23);(4,5)(10,11,15,18)(12,16,20,25)(13,17,14,22)(19,23,21,24);(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, 18570);