Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D13×C3⋊D123 |
| unambiguous semidirect product | (C3×D13)⋊D123 |
| unambiguous semidirect product | (D13×C41)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C13×C41 ⋊ C22 |
| Hall | C13×C41 ⋊ C2×C3⋊D3 |
| Hall | C32×C41 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D41 |
| Sylow | C41 ⋊ C3⋊D3×D13 |
| Sylow | C13 ⋊ C2×C3⋊D123 |
| Sylow | C32 ⋊ D13×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C41 | C22 |
| LCS | G ▷ C32×C13×C41 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4797 |
1488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 129);