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C₂×#33166 #6629988

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

Aliases

Subgroups

3806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6537184);