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C₂×#10944 #354113

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

Aliases

Subgroups

2894 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)(11,27)(12,16)(13,17)(14,20)(15,24)(19,28)(21,30)(22,29)(25,31)(26,37)(32,34)(33,36)(35,38);(7,9,12,20,13,22,11,21)(8,14,16,29,17,30,27,18)(10,19,25,33,26,35,24,34)(15,28,23,36,31,38,37,32);(4,6)(7,10,11,24,13,26,12,25)(8,15,16,23,17,31,27,37)(9,19,21,34,22,35,20,33)(14,28,29,36,30,38,18,32)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261309);