Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D9×D85 |
| unambiguous semidirect product | (C5×D9)⋊(C5×D17) |
| unambiguous semidirect product | (C17×D9)⋊(C5×D5) |
| Fitting, Hall | C52×C9×C17 ⋊ C22 |
| derived | C5×C9×C17 ⋊ C22×C5 |
| Hall | C52×C17 ⋊ C2×D9 |
| Hall | C52×C9 ⋊ C2×D17 |
| Hall | C9×C17 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ D9×D17 |
| Sylow | C17 ⋊ C5×D5×D9 |
| Sylow | C9 ⋊ C2×C5×D85 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D9×D85 |
| commutator, cosocle, hypocenter | C5×C9×C17 | C22×C5 |
| Frattini | C3 | C5×D3×D85 |
| Fitting | C52×C9×C17 | C22 |
| socle | C3×C52×C17 | C2×D3 |
| LCS | G ▷ C5×C9×C17 | |
| UCS | C1 ◁ C5 | |
144 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 144 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) = 1530 |
1320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 185);