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C₂×#1379 #12553

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

Aliases

Subgroups

303 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 38 points:

(1,2);(7,8,11,16,12,17,26,34,13,18,27,35,10,15,24,32)(9,19,21,36,20,30,37,33,22,31,25,38,23,14,28,29);(3,4,5,6)(7,9)(8,14)(10,23)(11,25)(12,20)(13,22)(15,31)(16,33)(17,19)(18,30)(21,27)(24,37)(26,28)(29,35)(32,36)(34,38)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 5541);