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C₂×#11336 #358478

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

Aliases

Subgroups

1998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265674);