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C₂×#1881 #20938

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

Aliases

Subgroups

841 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13926);