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C₂×#5771 #87186

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 37 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19762);