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C₂×#21550 #6372893

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

Aliases

Subgroups

2746 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)(9,18,22,28,19,33,21,14)(10,15,25,31,26,32,24,38)(20,34,36,30,23,37,35,29);(7,9,11,21,13,19,12,22)(8,14,16,18,17,28,27,33)(10,23,24,36,26,20,25,35)(15,30,31,37,32,29,38,34);(4,6)(9,19)(14,28)(18,33)(20,23)(21,22)(29,30)(34,37)(35,36);(7,10,12,25,13,26,11,24)(8,15,16,31,17,32,27,38)(9,20,22,36,19,23,21,35)(14,29,18,34,28,30,33,37)

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, 6280089);