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C₂×#11671 #481321

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

Aliases

Subgroups

994 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)(13,16)(14,23)(15,19)(17,20)(18,21)(22,25)(24,26);(3,5)(4,7)(6,8)(9,10)(12,16)(13,20)(14,21)(17,18)(19,25)(22,26)(23,24);(4,5)(8,9)

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, 388517);