Finite Group Databasebeta

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#30637368

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,127|a^2=e,b^2=f,c^2=g,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^126,d^b=dg,e^b=efg

Conjugacy classes & character table

1790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 3148);