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C₂×#11140 #357834

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

Aliases

Subgroups

2578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265030);