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C₂×#11599 #481062

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

Aliases

Subgroups

1256 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)(11,12,13,17,15,20,21,19)(14,23,22,18,25,16,24,26);(12,16)(13,21)(14,24)(17,18)(19,26)(20,23)(22,25);(11,13,15,21)(12,17,20,19)(14,22,25,24)(16,26,23,18)

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, 388258);