Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C5⋊D5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊(C3⋊#1039) |
| derived, Hall | C32×C52 ⋊ C4 |
| Sylow | C52 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ #1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊(C5⋊D5)) |
| commutator, hypocenter | C32×C52 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C52 | C2 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 900 |
Polycyclic presentation:
2^2,3^2,5^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^4228 conjugacy classes — view the full character table.
| maximal subgroup of | #14268211, #14268212, C3⋊Dic3×C5⋊D5, … |
| maximal normal subgroup of | #14268211, #14268212, C3⋊Dic3×C5⋊D5, … |
| maximal quotient of | C3⋊(C3⋊#6029), C2×C3⋊(C3⋊#1039), C13×C3⋊(C3⋊#1039), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 86);