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C₂×#11377 #358597

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

Aliases

Subgroups

2350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265793);