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C₂×#43414 #7667651

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

Aliases

Subgroups

5874 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)(13,14)(15,17)(16,18)(19,20,23,26)(21,24,22,25);(3,4)(5,10)(6,7)(8,9)(11,13,16,15)(12,17,18,14)(19,21,23,22)(20,24,26,25);(4,7)(8,10)(11,13,16,15)(12,14,18,17)(19,20)(21,24)(22,25)(23,26);(3,4)(5,8)(6,7)(9,10)(11,14,16,17)(12,13,18,15);(3,5)(4,8)(6,9)(7,10)(11,15,16,13)(12,17,18,14)(19,22,23,21)(20,25,26,24)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574847);