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C₂×#61685 #10577291

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

Aliases

Subgroups

7974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484487);