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C₂×#3011 #60363

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

Aliases

Subgroups

2359 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,6)(7,8,12,16)(9,17,20,30)(10,14,21,28)(11,23,25,15)(13,24,27,19)(18,31,32,38)(22,35,34,29)(26,36,37,33);(7,9,12,20)(8,13,16,27)(10,18,21,32)(11,24,25,19)(14,26,28,37)(15,30,23,17)(22,36,34,33)(29,38,35,31);(4,6)(7,10)(8,14)(9,18)(11,22)(12,21)(13,26)(15,29)(16,28)(17,31)(19,33)(20,32)(23,35)(24,36)(25,34)(27,37)(30,38);(10,21)(14,28)(18,32)(22,34)(26,37)(29,35)(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, 53351);