Finite Group DatabasebetaFinite Group Databasebeta| order | 18886 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19×C71 · Schur multiplier (H2) = C1 |
| direct product | D7×C19×C71 |
| unambiguous semidirect product | C7⋊(C2×C19×C71) |
| Fitting, socle, Hall | C7×C19×C71 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C19×C71 |
| Hall | C7×C71 ⋊ C2×C19 |
| Hall | C7×C19 ⋊ C2×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19×C71 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C19×C71 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C71 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C19×C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9443 |
6745 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C19×D71, D7×D19×C71, D7×D1349, … |
| maximal normal subgroup of | D7×C19×D71, D7×D19×C71, D7×D1349, … |
| maximal quotient of | C19×Dic7×C71, C2×D7×C19×C71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18886, 6);