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C₂×#12720 #493443

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

Aliases

Subgroups

2240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400639);