Finite Group Databasebeta

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C₂×#5644 #85977

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

(1,2)(3,4,5)(6,8)(7,11)(9,12)(10,13)(14,17,18,19)(15,16,20,21);(7,10)(11,13)(14,16,18,21)(15,19,20,17);(6,7)(8,11)(9,10)(12,13)(14,15)(16,17)(18,20)(19,21);(4,5)(8,12)(11,13)(16,21)(17,19);(1,2)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18553);