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C₂×#46890 #7700678

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

Aliases

Subgroups

5174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7607874);