Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×C3⋊#1039 |
| unambiguous semidirect product | C3⋊(C3×#1039) |
| derived | C3×C52 ⋊ C3×C4 |
| Hall | C32×C52 ⋊ C4 |
| Sylow | C52 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ #1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊(C5⋊D5) |
| commutator, hypocenter | C3×C52 | C3×C4 |
| Frattini | C2 | C3×C3⋊(C5⋊D5) |
| Fitting, socle, prime radical | C2×C32×C52 | C2 |
| cosocle | C2×C3×C52 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2×C3 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×C5⋊D5, C3×D3×#1039, C3×#10597114, … |
| maximal normal subgroup of | C3×Dic3×C5⋊D5, C3×D3×#1039, C3×#10597114, … |
| maximal quotient of | C3×C3⋊#6029, C2×C3×C3⋊#1039, C3⋊#16839052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 83);