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C₂×#12756 #493567

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

Aliases

Subgroups

2431 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)(5,15,19,30,18,31,16,32)(7,21,20,28,22,12,23,27)(10,24,25,17,26,33,29,34);(3,5)(4,10)(6,16)(7,17)(8,19)(9,18)(11,25)(12,15)(13,29)(14,26)(20,33)(21,31)(22,34)(23,24)(27,32)(28,30);(3,6,9,8)(4,11,14,13)(5,16,18,19)(7,20,22,23)(10,25,26,29)(12,28,21,27)(15,30,31,32)(17,33,34,24)

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, 400763);