Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#11925898) |
| Fitting, socle, derived, Hall | C32×C112 ⋊ C2×C5 |
| Hall | C32×#10597244 ⋊ C2 |
| Hall | C11×C3⋊D33 ⋊ C5 |
| Hall | #10597244 ⋊ C3⋊D3 |
| Sylow | C112 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ #11925898 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C112 | C2×C5 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 | |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3^2,11^2|c^a=c^2,d^a=d^2,e^a=e^10,e^b=e^4,f^b=f^5141 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊#11925898, #36345138, C3⋊D3×#11925898, … |
| maximal normal subgroup of | D3×C3⋊#11925898, #36345138, C3⋊D3×#11925898, … |
| maximal quotient of | C3⋊(C3⋊#14559057), C2×C3⋊(C3⋊#11925898) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 123);