Finite Group Databasebeta

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#29670468

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,61|b^2=gh,c^2=h,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,d^b=de,e^b=eg,i^b=i^60,f^c=fh,i^c=i^60,e^d=eg

Conjugacy classes & character table

820 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 160023);