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C₂×#9520 #201909

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

Aliases

Subgroups

2492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 109105);