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C₂×#1796 #20622

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

Aliases

Subgroups

1801 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 13610);