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C₂×#11680 #481341

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

Aliases

Subgroups

968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 388537);