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C₂×#18077 #6345119

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

Aliases

Subgroups

1656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252315);