Finite Group Databasebeta

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#34012223

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,73|a^2=e,b^2=f,d^2=gh,e^2=h,f^2=gh,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,i^a=i^46,d^b=dh,i^b=i^27,i^c=i^72,i^e=i^72,i^f=i^72

Conjugacy classes & character table

568 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1095807);