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C₂×#20599 #6370712

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

Aliases

Subgroups

18002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6277908);