Finite Group DatabasebetaFinite Group Databasebeta| order | 19270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D205 |
| unambiguous semidirect product | C5⋊(C47×D41) |
| unambiguous semidirect product | C41⋊(D5×C47) |
| Fitting, socle, Hall | C5×C41×C47 ⋊ C2 |
| derived, Hall | C5×C41 ⋊ C2×C47 |
| Hall | C41×C47 ⋊ D5 |
| Hall | C5×C47 ⋊ D41 |
| Sylow | C41 ⋊ D5×C47 |
| Sylow | C5 ⋊ C47×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D205 |
| commutator, cosocle, hypocenter | C5×C41 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C5×C41×C47 | C2 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9635 |
4888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#11717961, C47⋊#11717961, C47×#11717962, … |
| maximal normal subgroup of | C47×#11717961, C47⋊#11717961, C47×#11717962, … |
| maximal quotient of | C47×Dic205, C2×C47×D205 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19270, 8);