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C₂×#49247 #7704349

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

Aliases

Subgroups

7642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7611545);