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C₂×#23753 #6432448

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

Aliases

Subgroups

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339644);