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C₂×#34291 #7625604

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

Aliases

Subgroups

11114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532800);