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C₂×#12728 #493462

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

Aliases

Subgroups

2292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400658);