Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#11925890) |
| Fitting, socle, Hall | C32×C112 ⋊ D5 |
| derived, Hall | C32×#10597245 ⋊ C2 |
| Hall | #10597245 ⋊ C3⋊D3 |
| Sylow | C112 ⋊ C3⋊D15 |
| Sylow | C32 ⋊ #11925890 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×#10597245 | C2 |
| Fitting, socle | C32×C112 | D5 |
| LCS | G ▷ C32×#10597245 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,11^2|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^3f^3,f^a=ef^8,e^d=e^4f^8,f^d=f^3147 conjugacy classes — view the full character table.
| maximal subgroup of | #36345109, D3×C3⋊#11925890, #11925890⋊(C3⋊D3), … |
| maximal normal subgroup of | #36345109, D3×C3⋊#11925890, #11925890⋊(C3⋊D3), … |
| maximal quotient of | C3⋊(C3⋊#14559049), C2×C3⋊(C3⋊#11925890) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 129);