Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#14581472 |
| derived, Sylow | C73 ⋊ C4×C7×C9 |
| Hall | C7×#10620321 ⋊ C4 |
| Hall | C7×#64408 ⋊ C9 |
| Hall | #10620321 ⋊ C4×C7 |
| Hall | C7×C73 ⋊ C4×C9 |
| Hall | #64408 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #64408⋊C3 |
| commutator, hypocenter | C73 | C4×C7×C9 |
| Frattini | C3 | C7×#64408⋊C3 |
| Fitting, socle | C3×C7×C73 | C3×C4 |
| prime radical | C3×C7×D73 | C2×C3 |
| cosocle | C3×D73 | C2×C3×C7 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4599 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 26);