Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C11 |
| direct product | C5×C3⋊(C5⋊(C11⋊D11)) |
| unambiguous semidirect product | C3⋊(C5×C5⋊(C11⋊D11)) |
| unambiguous semidirect product | C5⋊(C5×C3⋊(C11⋊D11)) |
| Fitting, socle, Hall | C3×C52×C112 ⋊ C2 |
| derived | C3×C5×C112 ⋊ C2×C5 |
| Hall | C52×C112 ⋊ D3 |
| Hall | C3×C112 ⋊ C5×D5 |
| Sylow | C112 ⋊ C5×D15 |
| Hall | C3×C52 ⋊ C11⋊D11 |
| Sylow | C52 ⋊ C3⋊(C11⋊D11) |
| Sylow | C3 ⋊ C5×C5⋊(C11⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(C5⋊(C11⋊D11)) |
| commutator, cosocle, hypocenter | C3×C5×C112 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C112 | C2 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 ◁ C5 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3630 |
4545 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D11×D165, C5×D15×C11⋊D11, C5×D33×D55, … |
| maximal normal subgroup of | C5×D11×D165, C5×D15×C11⋊D11, C5×D33×D55, … |
| maximal quotient of | C5×C3⋊(C11⋊Dic55), C2×C5×C3⋊(C5⋊(C11⋊D11)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 191);