Finite Group Databasebeta

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#13097693

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

63 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 45);