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C₂×#21547 #6372896

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

Aliases

Subgroups

2722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6280092);