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C₂×#14240 #514757

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

Aliases

Subgroups

5290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421953);