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C₂×#17503 #6343010

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

Aliases

Subgroups

3494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250206);