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C₂×#46271 #7702884

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

Aliases

Subgroups

6202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 7610080);