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C₂×#19661 #6357155

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

Aliases

Subgroups

2970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6264351);