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C₂×#2957 #60181

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

Aliases

Subgroups

1321 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53169);