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C₂×#33594 #7622949

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

Aliases

Subgroups

2072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530145);