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C₂×#37034 #7634245

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

Aliases

Subgroups

6310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541441);