Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic693 |
| unambiguous semidirect product | C9⋊(C7⋊Dic77) |
| unambiguous semidirect product | C11⋊(C7⋊Dic63) |
| derived, Hall | C72×C9×C11 ⋊ C4 |
| Hall | C72×C11 ⋊ Dic9 |
| Hall | C72×C9 ⋊ Dic11 |
| Hall | C9×C11 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic99 |
| Sylow | C11 ⋊ C7⋊Dic63 |
| Sylow | C9 ⋊ C7⋊Dic77 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊D693 |
| commutator, hypocenter | C72×C9×C11 | C4 |
| Frattini | C2×C3 | C3⋊(C7⋊D77) |
| Fitting, cosocle | C2×C72×C9×C11 | C2 |
| socle, prime radical | C2×C3×C72×C11 | D3 |
| LCS | G ▷ C72×C9×C11 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19404 |
Polycyclic presentation:
2,3,7^2,11,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^6,d^a=d^6,e^a=e^10,g^a=g^24854 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 145);