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C₂×#5699 #86101

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 29 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18677);