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C₂×#4520 #71459

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 4035);