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C₂×#10711 #353156

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

Aliases

Subgroups

2466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260352);