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C₂×#5628 #85975

• supersolvable
• metabelian
• solvable
• monomial

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)(10,13)(11,17)(12,20)(14,22)(15,23)(16,18)(19,21)(24,25);(1,2)(7,9)(10,13,14,22)(11,16,18,17)(12,19,21,20)(15,23,24,25);(10,12,14,21)(11,15,18,24)(13,20,22,19)(16,25,17,23);(4,5)(10,11)(12,15)(13,16)(14,18)(17,22)(19,23)(20,25)(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, 18551);