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C₂×#23511 #6431898

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

Aliases

Subgroups

5606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339094);