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C₂×#33404 #7622527

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

Aliases

Subgroups

1890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529723);