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C₂×#11337 #358442

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

Aliases

Subgroups

1974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265638);