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C₂×#23504 #6431895

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

Aliases

Subgroups

5214 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)(11,12)(13,21)(14,18)(15,19)(16,20)(17,24)(22,25)(23,26);(7,8)(9,10)(11,12)(13,22)(14,18)(15,19)(16,20)(17,23)(21,25)(24,26);(4,6)(7,9,10,8)(11,13)(12,17)(14,23)(15,24)(16,25)(18,21)(19,22)(20,26);(11,14,16,15)(12,18,20,19)(13,23,25,24)(17,21,26,22)

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, 6339091);