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C₂×#1658 #18988

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

Aliases

Subgroups

441 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 11976);