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C₂×#555 #3473

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

Aliases

Subgroups

620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4)(5,9)(6,10)(7,8)(12,13)(16,17);(4,8)(6,9)(11,12,15,13)(14,17,18,16);(3,5,7,10)(4,9,8,6)(11,13,15,12)(14,17,18,16);(3,6,7,9)(4,10,8,5)(11,14,15,18)(12,16,13,17)

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2205);