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C₂×#4522 #71494

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 69 points:

(3,4,5)(6,8,12,22)(7,13,17,38)(9,24,28,58)(10,30,32,64)(11,34,31,21)(14,40,42,67)(15,44,45,69)(16,46,33,37)(18,47,49,23)(19,39,35,26)(20,43,52,25)(27,62,60,57)(29,36,63,65)(41,68,54,51)(48,55,53,61)(50,59,56,66);(4,5)(6,7,12,17)(8,18,22,49)(9,23,28,47)(10,29,32,63)(11,33,31,16)(13,35,38,19)(14,39,42,26)(15,43,45,25)(20,51,52,68)(21,53,34,48)(24,44,58,69)(27,61,60,55)(30,40,64,67)(36,62,65,57)(37,50,46,56)(41,59,54,66);(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, 4070);