Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×C17×D25 |
| unambiguous semidirect product | (D3×C25)⋊(C2×C3×C17) |
| unambiguous semidirect product | (C3×D25)⋊(C2×C3×C17) |
| unambiguous semidirect product | D75⋊(C2×C3×C17) |
| Fitting, Hall | C32×C17×C25 ⋊ C22 |
| derived | C3×C25 ⋊ C22×C3×C17 |
| Hall | C17×C25 ⋊ C2×C3×D3 |
| Hall | C32×C25 ⋊ C22×C17 |
| Hall | C32×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C3×D3×C17 |
| Sylow | C32 ⋊ C2×C17×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | D3×D25 |
| commutator, cosocle, hypocenter | C3×C25 | C22×C3×C17 |
| Frattini | C5 | C3×D3×D5×C17 |
| Fitting | C32×C17×C25 | C22 |
| socle | C32×C5×C17 | C2×D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C3×C17 | |
132 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2550 |
2142 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 83);