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C₂×#33716 #7623190

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

Aliases

Subgroups

2482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530386);