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C₂×#5712 #86109

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

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)(15,21)(16,23)(17,25)(26,28);(6,7)(8,11)(9,10)(12,13)(14,17)(15,20)(16,22)(18,25)(19,26)(21,24)(23,29)(27,28);(7,10)(11,13)(14,16,18,23)(15,19,21,27)(17,22,25,29)(20,26,24,28);(4,5)(8,12)(11,13)(14,15)(16,19)(17,24)(18,21)(20,25)(22,28)(23,27)(26,29);(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, 18685);