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C₂×#46616 #7700152

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

Aliases

Subgroups

6320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 7607348);