Finite Group DatabasebetaFinite Group Databasebeta| order | 31668 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊Dic377 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)⋊D377 |
| commutator, hypocenter | C7×C13×C29 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C13×C29 | C2×C3 |
| prime radical | C2×C13×ΓL(1,𝔽8)×C29 | C2 |
| LCS | G ▷ C7×C13×C29 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10556 |
Polycyclic presentation:
2,3,7,13,29,2|a^2=f,c^a=c^6,d^a=d^12,e^a=e^28,c^b=c^21894 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31668, 55);