Finite Group DatabasebetaFinite Group Databasebeta| order | 18050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D361 |
| unambiguous semidirect product | C361⋊(C2×C52) |
| Fitting, Hall | C52×C361 ⋊ C2 |
| derived, Sylow | C361 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D361 |
| commutator, cosocle, hypocenter | C361 | C2×C52 |
| Frattini | C19 | C52×D19 |
| Fitting | C52×C361 | C2 |
| socle | C52×C19 | D19 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C52 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9025 |
4550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D5×D361, C5⋊D5×D361, C2×C52×D361 |
| maximal normal subgroup of | C5×D5×D361, C5⋊D5×D361, C2×C52×D361 |
| maximal quotient of | C52×Dic361, C2×C52×D361 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18050, 6);