Finite Group Databasebeta

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C₂²⋊#622 #63787

• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 18 points:

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

Polycyclic presentation:

2^5,3^2|a^2=c,c^2=e,b^a=bd,f^a=fg^2,g^a=f^2g^2,f^c=f^2,g^c=g^2

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 435);