Finite Group DatabasebetaFinite Group Databasebeta| order | 37485 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×#89204 |
| derived, Sylow | C72 ⋊ C5×C9×C17 |
| Hall | C5×C72×C17 ⋊ C9 |
| Hall | C72×C17 ⋊ C5×C9 |
| Hall | C5×C72 ⋊ C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C17 | #3861 |
| commutator, hypocenter | C72 | C5×C9×C17 |
| Frattini | C3 | C5×C17×#3861 |
| Fitting, socle, prime radical | C3×C5×C72×C17 | C3 |
| cosocle | C3×C72 | C3×C5×C17 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C5×C17 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37485 |
4845 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37485, 8);