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C₂×#12541 #492830

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

Aliases

Subgroups

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400026);