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C₂×#11119 #357786

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

Aliases

Subgroups

2690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264982);