Finite Group Databasebeta

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C₂×#5646 #85972

• 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)(7,11)(9,12)(10,13)(14,17,18,26)(15,21,22,29)(16,23,24,25)(19,27,20,28);(6,7)(8,11)(9,10)(12,13)(14,16)(15,20)(17,23)(18,24)(19,22)(21,28)(25,26)(27,29);(7,10)(11,13)(14,16,18,24)(15,19,22,20)(17,25,26,23)(21,28,29,27);(4,5)(8,12)(11,13)(14,15)(16,19)(17,21)(18,22)(20,24)(23,27)(25,28)(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, 18548);