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C₂×#23875 #6437582

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

Aliases

Subgroups

5950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344778);