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C₂×#12586 #492904

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

Aliases

Subgroups

2338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400100);