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C₂×#33349 #7622448

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

Aliases

Subgroups

4152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529644);