Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#11725071⋊C2 |
| unambiguous semidirect product | #11725071⋊(C2×C11) |
| derived, Hall | #89205 ⋊ C22×C11 |
| Hall | C11×#89205 ⋊ C22 |
| Hall | C72×C11 ⋊ C2×D9 |
| Sylow | C72 ⋊ C2×C11×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #11725071⋊C2 |
| commutator, cosocle, hypocenter | #89205 | C22×C11 |
| Frattini | C3 | C11×#64418⋊C2 |
| Fitting, socle | C3×C72×C11 | C2×D3 |
| LCS | G ▷ #89205 | |
| UCS | C1 ◁ C11 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 693 |
363 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 164);