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C₂×#5838 #87288

• 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:

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19864);