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C₂×#17327 #6342449

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

Aliases

Subgroups

2472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6249645);