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C₂×#9425 #200836

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

Aliases

Subgroups

1494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 108032);