Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×#10620323⋊C2 |
| unambiguous semidirect product | #10620323⋊(C22×C7) |
| unambiguous semidirect product | (C2×#10620323)⋊(C2×C7) |
| Fitting, socle | C2×C7×C73 ⋊ C2×C9 |
| derived, Sylow | C73 ⋊ C22×C7×C9 |
| Hall | C7×#10620323 ⋊ C22 |
| Hall | C2×C7×D73 ⋊ C9 |
| Hall | #10620323 ⋊ C22×C7 |
| Hall | C7×C73 ⋊ C22×C9 |
| Hall | C2×D73 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | #10620323⋊C2 |
| commutator, hypocenter | C73 | C22×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C73 | C2×C9 |
| prime radical | C2×C7×D73⋊C3 | C3 |
| cosocle | C73⋊C3 | C22×C3×C7 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1022 |
308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 150);