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C₂×#20180 #6359531

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

Aliases

Subgroups

1689 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266727);