Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | D33⋊#64425 |
| Fitting, socle, derived | C3×C72×C11 ⋊ C22×C3 |
| Hall | C3×C11×#3862 ⋊ C22 |
| Hall | C72×C11 ⋊ C2×C3×D3 |
| Hall | C3×#3862 ⋊ C2×D11 |
| Sylow | C72 ⋊ C3×D3×D11 |
| Sylow | C11 ⋊ D3×#64425 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C11 | C22×C3 |
| LCS | G ▷ C3×C72×C11 | |
| UCS | C1 | |
216 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 693 |
Polycyclic presentation:
2^2,3^2,7^2,11|e^a=e^6,f^a=f^6,g^a=g^10,d^b=d^2,e^b=e^6,f^b=f^6,e^c=e^2,f^c=f^4207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 365);