Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D153⋊(C5⋊D5) |
| Fitting, derived, Hall | C52×C9×C17 ⋊ C22 |
| Hall | C52×C17 ⋊ C2×D9 |
| Hall | C52×C9 ⋊ C2×D17 |
| Hall | C9×C17 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ D9×D17 |
| Sylow | C17 ⋊ D9×C5⋊D5 |
| Sylow | C9 ⋊ D17×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C17 | C22 |
| Frattini | C3 | D51⋊(C5⋊D5) |
| socle | C3×C52×C17 | C2×D3 |
| LCS | G ▷ C52×C9×C17 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3825 |
Polycyclic presentation:
2^2,3,5^2,17,3|c^3=g^2,d^a=d^4,e^a=e^4,f^a=f^16,c^b=c^2g,d^b=d^4,e^b=e^4,g^b=g^2996 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 203);