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C₂×#45701 #7702084

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

Aliases

Subgroups

7262 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)(19,20,23,24)(21,25,26,22);(4,7)(5,9)(12,16)(17,18)(20,24)(21,26);(3,4)(5,8)(6,7)(9,10)(11,13,15,14)(12,17,16,18)(19,21,23,26)(20,25,24,22);(3,5)(4,8)(6,9)(7,10)(11,12)(13,17)(14,18)(15,16)(19,22,23,25)(20,26,24,21);(3,4)(5,8)(6,7)(9,10)(11,14,15,13)(12,18,16,17)(19,20)(21,25)(22,26)(23,24)

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, 7609280);