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C₂×#33392 #7622511

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

Aliases

Subgroups

4064 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529707);