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C₂×#33463 #7622623

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

Aliases

Subgroups

1932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529819);