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C₂×#59382 #7665907

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

Aliases

Subgroups

7702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573103);