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C₂×#61060 #10576072

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

Aliases

Subgroups

10434 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)(11,25)(12,15)(13,20)(16,26)(18,33)(19,29)(21,28)(22,36)(23,37)(24,31)(27,35)(30,34)(32,38);(7,9,12,21)(8,13,15,29)(10,22,24,18)(11,19,26,20)(14,30,31,27)(16,28,25,17)(23,35,38,34)(32,33,37,36);(4,6)(7,10,12,24)(8,14,15,31)(9,18,21,22)(11,23,26,38)(13,27,29,30)(16,32,25,37)(17,33,28,36)(19,34,20,35);(9,19)(11,26)(13,28)(16,25)(17,29)(18,34)(20,21)(22,35)(23,38)(27,36)(30,33)(32,37);(8,15)(13,29)(14,31)(16,25)(17,28)(27,30)(32,37)(33,36)

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, 10483268);