Finite Group DatabasebetaFinite Group Databasebeta| order | 18886 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C71 · Schur multiplier (H2) = C1 |
| direct product | C7×D19×C71 |
| unambiguous semidirect product | C19⋊(C2×C7×C71) |
| Fitting, socle, Hall | C7×C19×C71 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C7×C71 |
| Hall | C19×C71 ⋊ C2×C7 |
| Hall | C7×C19 ⋊ C2×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C71 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C7×C71 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C71 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C7×C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9443 |
5467 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D71, D7×D19×C71, D19×D497, … |
| maximal normal subgroup of | C7×D19×D71, D7×D19×C71, D19×D497, … |
| maximal quotient of | C7×C71×Dic19, C2×C7×D19×C71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18886, 4);