Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11725071⋊D11 |
| derived, Hall | C11×#89205 ⋊ C22 |
| Hall | C72×C11 ⋊ C2×D9 |
| Hall | #89205 ⋊ C2×D11 |
| Sylow | C72 ⋊ D9×D11 |
| Sylow | C11 ⋊ #11725071⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×#89205 | C22 |
| Frattini | C3 | #64418⋊D11 |
| Fitting, socle | C3×C72×C11 | C2×D3 |
| LCS | G ▷ C11×#89205 | |
| UCS | C1 | |
112 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 17 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:
2^2,3,11,7^2,3|c^3=g^2,c^a=c^2g,d^a=d^10,e^a=e^4f,f^a=e^6f^3,g^a=g^2,c^b=c^2g,e^b=e^3f^6,f^b=ef^4,g^b=g^2,e^c=e^2f^6,f^c=f^4228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 165);