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C₂×#33834 #7623581

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

Aliases

Subgroups

2070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530777);