Finite Group Databasebeta

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#36322320

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,167|a^2=d,b^2=g,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^166,c^b=ce,e^b=ef,f^b=fg,h^b=h^166

Conjugacy classes & character table

5350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 2692);