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C₂×#1915 #21016

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

Aliases

Subgroups

835 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 14004);