Finite Group DatabasebetaFinite Group Databasebeta| order | 3630 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#11925890 |
| Fitting, socle, Hall | C3×C112 ⋊ D5 |
| derived, Hall | C3×#10597245 ⋊ C2 |
| Hall | #10597245 ⋊ D3 |
| Sylow | C112 ⋊ D15 |
| Sylow | C3 ⋊ #11925890 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#10597245 | C2 |
| Fitting, socle | C3×C112 | D5 |
| LCS | G ▷ C3×#10597245 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 66 |
Polycyclic presentation:
2,3,5,11^2|b^a=b^2,c^a=c^4,d^a=d^3e^3,e^a=de^8,d^c=d^4e^8,e^c=e^360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3630, 42);