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C₂×#61051 #10576063

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

Aliases

Subgroups

10586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 38 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483259);