Finite Group Databasebeta

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#13097891

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

93 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,5^2|a^2=c,c^2=f,d^2=e,e^2=f,g^5=h,b^a=bd,d^a=de,e^a=ef,g^a=g^2h,h^a=h^2,c^b=cf,d^b=def,e^b=ef,g^c=g^4h^4,h^c=h^4

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 243);