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C₂×#11090 #357767

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

Aliases

Subgroups

2658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264963);