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C₂×#3069 #60468

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

Aliases

Subgroups

1309 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53456);