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C₂×#33600 #7622959

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

Aliases

Subgroups

2106 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)(9,18)(10,15)(11,25)(12,27)(13,17)(14,21)(16,19)(20,31)(22,37)(23,33)(24,30)(26,38)(28,35)(29,36)(32,34);(7,9,19,34,12,22,26,36,13,23,24,35,10,20,11,21)(8,14,25,31,15,28,30,33,17,29,38,37,27,32,16,18);(4,6);(7,10,13,12)(8,15,17,27)(9,20,23,22)(11,24,26,19)(14,28,29,32)(16,25,30,38)(18,31,33,37)(21,35,36,34)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530155);