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C₂×#20299 #6361237

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

Aliases

Subgroups

1718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6268433);