Finite Group Databasebeta

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#32068123

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,71|a^2=eh,d^2=ef,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^70,c^b=cg,e^b=eh,f^b=fh,e^c=eh,f^c=fh,e^d=eh,f^d=fh

Conjugacy classes & character table

1802 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 240239);