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C₂×#37626 #7633888

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

Aliases

Subgroups

7102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541084);