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C₂×#13024 #494530

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

Aliases

Subgroups

1300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401726);