Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D25 |
| unambiguous semidirect product | D75⋊D3 |
| Fitting, derived, Hall | C32×C25 ⋊ C22 |
| Sylow | C25 ⋊ D32 |
| Sylow | C32 ⋊ C2×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C25 | C22 |
| Frattini | C5 | (C3⋊D3)⋊D5 |
| socle | C32×C5 | C2×D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
Polycyclic presentation:
2^2,3^2,5^2|e^5=f,c^a=c^2,e^a=e^4f^4,f^a=f^4,c^b=c^2,d^b=d^281 conjugacy classes — view the full character table.
| maximal subgroup of | D32⋊D25, #157⋊D25, D32×D25, … |
| maximal normal subgroup of | D32⋊D25, #157⋊D25, D32×D25, … |
| maximal quotient of | #14267898, #14267899, #14267900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 38);