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C₂×#33720 #7623195

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

Aliases

Subgroups

2586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530391);