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C₂×#23362 #6407633

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

Aliases

Subgroups

2044 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6314829);