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C₂×#7988 #181261

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

Aliases

Subgroups

1726 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)(11,12,14,18,16,20,15,19)(13,21,22,17,24,25,23,26);(4,7)(5,9)(11,13,15,23,16,24,14,22)(12,17,18,25,20,26,19,21);(11,14,16,15)(12,18,20,19)(13,22,24,23)(17,25,26,21)

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, 88457);