Finite Group DatabasebetaFinite Group Databasebeta| order | 18837 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C23 · Schur multiplier (H2) = C3 |
| direct product | C3×C23×#63271 |
| Fitting, socle | C3×C7×C13×C23 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C32×C23 |
| Hall | C7×C13×C23 ⋊ C32 |
| Hall | C13×C23 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C23 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×ΓL(1,𝔽8)×C23 |
| Sylow | C7 ⋊ C3×C23×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | #63271 |
| commutator, cosocle, hypocenter | C7×C13 | C32×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C23 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C23 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6279 |
2277 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×#10587723, C3×C23⋊#10587723, C3×C23×#10587721, … |
| maximal normal subgroup of | C3×C23×#10587723, C3×C23⋊#10587723, C3×C23×#10587721, … |
| maximal quotient of | C2×C3×C23×#63271 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18837, 9);