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C₂×#12710 #493401

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

Aliases

Subgroups

3316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400597);