Finite Group DatabasebetaFinite Group Databasebeta| order | 18050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D1805 |
| unambiguous semidirect product | C361⋊(C5⋊D5) |
| Fitting, derived, Hall | C52×C361 ⋊ C2 |
| Sylow | C361 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C361 | C2 |
| Frattini | C19 | C5⋊D95 |
| socle | C52×C19 | D19 |
| LCS | G ▷ C52×C361 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9025 |
Polycyclic presentation:
2,5^2,19^2|d^19=e^18,b^a=b^4,c^a=c^4,d^a=d^18e,e^a=e^184514 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊D5×D361, D5×D1805, C2×C5⋊D1805 |
| maximal normal subgroup of | C5⋊D5×D361, D5×D1805, C2×C5⋊D1805 |
| maximal quotient of | C361⋊#1039, C2×C5⋊D1805 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18050, 10);