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C₂×#28938 #6460039

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

Aliases

Subgroups

2416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6367235);