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C₂×#33719 #7623193

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

Aliases

Subgroups

2514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530389);