Finite Group DatabasebetaFinite Group Databasebeta| order | 16245 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×#11762245⋊C5 |
| unambiguous semidirect product | (C192⋊C5)⋊C32 |
| unambiguous semidirect product | (C3×#11762245)⋊C5 |
| unambiguous semidirect product | (C3×C192⋊C5)⋊C3 |
| Fitting, socle | C3×C192 ⋊ C3×C5 |
| derived, Sylow | C192 ⋊ C32×C5 |
| Hall | C3×#11762245 ⋊ C5 |
| Hall | C192⋊C5 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11762245⋊C5 |
| commutator, cosocle, hypocenter | C192 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C192 | C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 285 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16813380⋊C3, C3×#14524206⋊C5, D3×#11762245⋊C5, … |
| maximal normal subgroup of | C3×#16813380⋊C3, C3×#14524206⋊C5, D3×#11762245⋊C5, … |
| maximal quotient of | C2×C3×#11762245⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16245, 14);