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C₂×#48550 #7703279

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

Aliases

Subgroups

7492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610475);