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C₂×#31408 #7504610

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

Aliases

Subgroups

2502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411806);