Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | (C3⋊D3)⋊(C5⋊D85) |
| Fitting, socle, derived, Hall | C32×C52×C17 ⋊ C22 |
| Hall | C52×C17 ⋊ D32 |
| Hall | C32×C52 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ (C3⋊D3)⋊D17 |
| Sylow | C17 ⋊ (C3⋊D3)⋊(C5⋊D5) |
| Sylow | C32 ⋊ C2×C5⋊D85 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52×C17 | C22 |
| LCS | G ▷ C32×C52×C17 | |
| UCS | C1 | |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2550 |
Polycyclic presentation:
2^2,3^2,5^2,17|d^a=d^2,e^a=e^4,f^a=f^4,g^a=g^16,c^b=c^2,d^b=d^21281 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 422);