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C₂×#23795 #6432580

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

Aliases

Subgroups

2742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339776);