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C₂×#45716 #7702142

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

Aliases

Subgroups

6930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609338);