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C₂×#3044 #60419

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

Aliases

Subgroups

1333 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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, 53407);