Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C73 ⋊ C4×C9 |
| Hall | #17987160 ⋊ C4 |
| Hall | C7×Dic73 ⋊ C9 |
| Hall | Dic73 ⋊ C7⋊C9 |
| Sylow | C73 ⋊ C4×C7⋊C9 |
| Sylow | C7 ⋊ #14581466 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | #15690442 |
| commutator, hypocenter | C7×C73 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C73 | C2×C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18396 |
Polycyclic presentation:
2,3,7,73,2,3|a^2=e,b^3=f,d^a=d^72,c^b=c^2,d^b=d^64564 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 16);