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C₂×#11414 #479957

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

Aliases

Subgroups

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387153);