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C₂×#11361 #358611

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

Aliases

Subgroups

1654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265807);