Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C7⋊(C7⋊(C11⋊#157)) |
| unambiguous semidirect product | C11⋊(C7⋊(C7⋊#157)) |
| Fitting, socle, derived, Hall | C32×C72×C11 ⋊ C4 |
| Hall | C72×C11 ⋊ #157 |
| Hall | C32×C72 ⋊ Dic11 |
| Hall | C32×C11 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C11⋊#157 |
| Sylow | C11 ⋊ C7⋊(C7⋊#157) |
| Sylow | C32 ⋊ C7⋊Dic77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C72×C11 | C4 |
| prime radical, cosocle | C72×C11×C3⋊D3 | C2 |
| LCS | G ▷ C32×C72×C11 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3234 |
Polycyclic presentation:
2^2,3^2,7^2,11|a^2=b,c^a=cd,d^a=cd^2,e^a=e^6,f^a=f^6,g^a=g^10,c^b=c^2,d^b=d^21620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 554);