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C₂×#18255 #6346551

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

Aliases

Subgroups

4234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253747);