Finite Group DatabasebetaFinite Group Databasebeta| order | 18963 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#20263467 |
| Fitting | C3×C43×C49 ⋊ C3 |
| derived, Hall | C43×C49 ⋊ C32 |
| Sylow | C49 ⋊ C3×C43⋊C3 |
| Sylow | C43 ⋊ C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20263467 |
| commutator, cosocle, hypocenter | C43×C49 | C32 |
| Frattini | C7 | C3×#11744749 |
| Fitting | C3×C43×C49 | C3 |
| socle | C3×C7×C43 | ΓL(1,𝔽8) |
| LCS | G ▷ C43×C49 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6321 |
2115 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#27162354, C3×#27162352, C3×#27162348, … |
| maximal normal subgroup of | C3×#27162354, C3×#27162352, C3×#27162348, … |
| maximal quotient of | C2×C3×#20263467 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18963, 14);