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C₂×#12611 #492963

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

Aliases

Subgroups

1302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400159);