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C₂×#8516 #187746

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

Aliases

Subgroups

4140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 94942);