Finite Group DatabasebetaFinite Group Databasebeta| order | 18990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((D211⋊C3)⋊C5) |
| unambiguous semidirect product | ((C211⋊C3)⋊C5)⋊D3 |
| unambiguous semidirect product | (C3⋊(D211⋊C3))⋊C5 |
| unambiguous semidirect product | (C3⋊(D211⋊C5))⋊C3 |
| Fitting, socle, derived | C3×C211 ⋊ C2×C3×C5 |
| Hall | C3×(C211⋊C3)⋊C5 ⋊ C2 |
| Hall | C3⋊(D211⋊C3) ⋊ C5 |
| Hall | C3×C211⋊C3 ⋊ C2×C5 |
| Hall | C211⋊C5 ⋊ C3×D3 |
| Sylow | C211 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C211 | C2×C3×C5 |
| LCS | G ▷ C3×C211 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 633 |
Polycyclic presentation:
2,3,5,3,211|d^a=d^2,e^a=e^210,e^b=e^14,e^c=e^18866 conjugacy classes — view the full character table.
| maximal subgroup of | D3×(D211⋊C3)⋊C5, C2×C3⋊((D211⋊C3)⋊C5) |
| maximal normal subgroup of | D3×(D211⋊C3)⋊C5, C2×C3⋊((D211⋊C3)⋊C5) |
| maximal quotient of | C3⋊(((C211⋊C3)⋊C4)⋊C5), C2×C3⋊((D211⋊C3)⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18990, 21);