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C₂×#41492 #7639653

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

Aliases

Subgroups

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546849);