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C₂×#33754 #7623285

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12)(13,21)(14,19)(15,18)(16,17)(20,24)(22,25)(23,26);(3,5)(4,7)(6,10)(8,9)(11,13,14,16)(12,17,19,21)(15,22,23,24)(18,20,26,25);(5,10)(7,9)(12,18)(13,16)(15,24)(17,25)(19,26)(20,21)(22,23);(4,8)(7,9)(12,19)(17,21)(18,26)(20,25)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530481);