Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D25×D51 |
| unambiguous semidirect product | (C3×D25)⋊(C3×D17) |
| unambiguous semidirect product | (C17×D25)⋊(C3×D3) |
| Fitting, Hall | C32×C17×C25 ⋊ C22 |
| derived | C3×C17×C25 ⋊ C22×C3 |
| Hall | C17×C25 ⋊ C2×C3×D3 |
| Hall | C32×C25 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C3×D51 |
| Sylow | C17 ⋊ C3×D3×D25 |
| Sylow | C32 ⋊ D17×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×D51 |
| commutator, cosocle, hypocenter | C3×C17×C25 | C22×C3 |
| Frattini | C5 | C3×D5×D51 |
| Fitting | C32×C17×C25 | C22 |
| socle | C32×C5×C17 | C2×D5 |
| LCS | G ▷ C3×C17×C25 | |
| UCS | C1 ◁ C3 | |
132 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2550 |
1134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 84);