Finite Group Databasebeta

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#31885115

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,71|a^2=d,b^2=eg,c^2=fgh,d^2=efgh,e^2=h,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eh,f^a=fh,i^a=i^70,c^b=cf,d^b=def,e^b=eh,f^b=fg,g^b=gh

Conjugacy classes & character table

1367 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 57231);