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C₂×#5766 #87181

• supersolvable
• metabelian
• solvable
• monomial

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)(6,9,11,21)(7,14,12,26)(8,16,18,34)(10,23,24,20)(13,28,25,36)(15,33,27,31)(17,35,22,19)(29,37,32,30);(1,2)(6,8,11,18)(7,13,12,25)(9,19,21,35)(10,22,24,17)(14,30,26,37)(15,32,27,29)(16,23,34,20)(28,33,36,31);(7,12)(13,25)(14,26)(15,27)(28,36)(29,32)(30,37)(31,33);(4,5)(6,7)(8,13)(9,14)(10,15)(11,12)(16,28)(17,29)(18,25)(19,30)(20,31)(21,26)(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, 19757);