Finite Group DatabasebetaFinite Group Databasebeta| order | 19350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | (C43⋊C3)⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C5⋊(C5⋊(D43⋊C3)))⋊C3 |
| unambiguous semidirect product | #20264541⋊C3 |
| unambiguous semidirect product | #20264543⋊C3 |
| Fitting, socle, derived, Hall | C52×C43 ⋊ C2×C32 |
| Hall | C52⋊C3×C43⋊C3 ⋊ C2 |
| Hall | C5⋊D215 ⋊ C32 |
| Sylow | C43 ⋊ C3×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C3×D43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C43 | C2×C32 |
| LCS | G ▷ C52×C43 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 645 |
Polycyclic presentation:
2,3^2,5^2,43|d^a=d^4,e^a=e^4,f^a=f^42,f^b=f^36,d^c=de,e^c=d^2e^3107 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19350, 64);