Finite Group DatabasebetaFinite Group Databasebeta| order | 18963 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×#11744748⋊C7 |
| unambiguous semidirect product | (C3×#11744748)⋊C7 |
| Fitting, socle | C3×C7×C43 ⋊ C3×C7 |
| derived | C7×C43 ⋊ C32×C7 |
| Hall | C7×C43⋊C7 ⋊ C32 |
| Sylow | C43 ⋊ C3×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11744748⋊C7 |
| commutator, cosocle, hypocenter | C7×C43 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C43 | C3×C7 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 903 |
147 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14268593⋊C7, C3×#14268591⋊C7, C3×#14268587⋊C7, … |
| maximal normal subgroup of | C3×#14268593⋊C7, C3×#14268591⋊C7, C3×#14268587⋊C7, … |
| maximal quotient of | C2×C3×#11744748⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18963, 35);