Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C3⋊#64408 |
| unambiguous semidirect product | C3⋊(C3×C7×#64408) |
| Fitting, socle, Hall | C32×C7×C73 ⋊ C4 |
| derived | C3×C73 ⋊ C3×C4×C7 |
| Hall | C32×C73 ⋊ C4×C7 |
| Hall | C7×C73 ⋊ C3×Dic3 |
| Sylow | C73 ⋊ C3×C7×Dic3 |
| Hall | C32×C7 ⋊ #64408 |
| Sylow | C32 ⋊ C7×#64408 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C3⋊#64408 |
| commutator, hypocenter | C3×C73 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C73 | C4 |
| prime radical | C32×C7×D73 | C2 |
| cosocle | C3×D73 | C2×C3×C7 |
| LCS | G ▷ C3×C73 | |
| UCS | C1 ◁ C3×C7 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3066 |
1260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 252);