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C₂×#1912 #21011

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

Aliases

Subgroups

847 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 13999);