Finite Group Databasebeta

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#35322990

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,83|a^2=f,b^2=defg,c^2=e,d^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^82,d^b=dg,f^b=fg,g^b=gh,i^b=i^82

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 88154);