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C₂×#9532 #202133

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

Aliases

Subgroups

1210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,6,9,8,12,7,11)(5,13,14,10,15,17,16,18)(19,20,25,28)(21,24,27,23)(22,29)(26,30)(31,33)(32,34);(4,9,12,11)(10,17,18,13)(19,21,23,20,25,27,24,28)(22,29,31,26,32,34,30,33);(3,5)(4,10)(6,14)(7,16)(8,15)(9,17)(11,13)(12,18)(19,22)(20,26)(21,29)(23,31)(24,30)(25,32)(27,34)(28,33)

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, 109329);