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C₂×#40414 #7638038

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

Aliases

Subgroups

7626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7545234);