Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×C3⋊#13133347 |
| unambiguous semidirect product | C3⋊(C3×#13133347) |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C4 |
| derived | C3×C52×C17 ⋊ C3×C4 |
| Hall | C52×C17 ⋊ C3×Dic3 |
| Hall | C32×C52 ⋊ #595 |
| Hall | C32×C17 ⋊ #1044 |
| Sylow | C52 ⋊ C3×C3⋊#595 |
| Sylow | C17 ⋊ C3×C3⋊#1044 |
| Sylow | C32 ⋊ #13133347 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#13133347 |
| commutator, hypocenter | C3×C52×C17 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C4 |
| prime radical | C32×C5⋊D85 | C2 |
| cosocle | C3×C5⋊D85 | C2×C3 |
| LCS | G ▷ C3×C52×C17 | |
| UCS | C1 ◁ C3 | |
160 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 510 |
972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 351);