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C₂×#59196 #7665805

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

Aliases

Subgroups

6694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7573001);