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C₂×#23414 #6431742

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

Aliases

Subgroups

7290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338938);