Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#10620323⋊D7 |
| unambiguous semidirect product | (C2×#10620323)⋊D7 |
| Fitting, socle | C2×C7×C73 ⋊ C2×C9 |
| derived, Hall | C7×C73 ⋊ C22×C9 |
| Hall | C7×#10620323 ⋊ C22 |
| Hall | C2×D511 ⋊ C9 |
| Hall | #10620323 ⋊ C2×D7 |
| Sylow | C73 ⋊ C2×C9×D7 |
| Sylow | C7 ⋊ C2×#10620323⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10620323⋊D7 |
| commutator, hypocenter | C7×C73 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C73 | C2×C9 |
| prime radical | C2×(C73⋊C3)⋊D7 | C3 |
| cosocle | C7×C73⋊C3 | C22×C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1022 |
146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 160);