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C₂×#32950 #6629047

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

Aliases

Subgroups

4438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6536243);