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C₂×#33401 #7622523

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

Aliases

Subgroups

2040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529719);