Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D5×C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived, Hall | C32×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×C3⋊D3 |
| Sylow | C32 ⋊ #6036 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C3⋊D15 |
| commutator, hypocenter | C32×C52 | C2×C4 |
| Fitting, socle, cosocle | C2×C32×C52 | C22 |
| prime radical | C2×C3⋊(C3⋊(C5⋊D5)) | C2 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^3,3^2,5^2|a^2=c,b^2=c,d^a=d^2,e^a=e^2,f^a=f^4,g^b=g^4192 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#6036, C2×#14268262, #72231168, … |
| maximal normal subgroup of | C3⋊D3×#6036, C2×#14268262, #72231168, … |
| maximal quotient of | C2×#14268262 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 456);