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C₂×#16557 #611126

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

Aliases

Subgroups

7934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518322);