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C₂×#52294 #7633640

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

Aliases

Subgroups

7892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540836);