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C₂×#23746 #6432439

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

Aliases

Subgroups

2382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339635);