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C₂×#8604 #188778

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

Aliases

Subgroups

1260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 95974);