Finite Group Databasebeta

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Dic₇₁₅₆ #43270402

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1805 points:

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Polycyclic presentation:

2^4,1789|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1788,c^b=cd,e^b=e^1788

Conjugacy classes & character table

7159 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28624, 31);