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C₂×#5583 #85809

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1004 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)(15,21,20,24)(16,23,22,28)(19,26,27,29);(6,7,9,10)(8,11,12,13)(15,20)(16,22)(21,24)(23,28);(14,16,18,22)(15,19,20,27)(17,23,25,28)(21,26,24,29);(4,5)(7,10)(11,13)(14,15)(16,19)(17,24)(18,20)(21,25)(22,27)(23,29)(26,28);(1,2)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18385);