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C₂×#9670 #204432

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

Aliases

Subgroups

1376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 111628);