Finite Group DatabasebetaFinite Group Databasebeta| order | 11850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊D395) |
| unambiguous semidirect product | C5⋊D1185 |
| unambiguous semidirect product | C79⋊(C3⋊(C5⋊D5)) |
| Fitting, socle, derived, Hall | C3×C52×C79 ⋊ C2 |
| Hall | C52×C79 ⋊ D3 |
| Hall | C3×C79 ⋊ C5⋊D5 |
| Sylow | C79 ⋊ C3⋊(C5⋊D5) |
| Hall | C3×C52 ⋊ D79 |
| Sylow | C52 ⋊ D237 |
| Sylow | C3 ⋊ C5⋊D395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C79 | C2 |
| LCS | G ▷ C3×C52×C79 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,79|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^782964 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1185, D15×D395, C3⋊(C5⋊D5)×D79, … |
| maximal normal subgroup of | D5×D1185, D15×D395, C3⋊(C5⋊D5)×D79, … |
| maximal quotient of | C3⋊(C79⋊#1039), C2×C3⋊(C5⋊D395), C5⋊D3555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11850, 30);