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C₂×#2143 #33384

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

Aliases

Subgroups

577 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 26372);