Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C73 ⋊ C4×C9 |
| Hall | #17987163 ⋊ C4 |
| Hall | C7⋊#64408 ⋊ C9 |
| Sylow | C73 ⋊ Dic7⋊C9 |
| Sylow | C7 ⋊ #14581496 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C4×C9 |
| prime radical, cosocle | C7×D73⋊C3 | C2×C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 511 |
Polycyclic presentation:
2,3,2,3,7,73|a^2=c,b^3=d,e^a=e^6,f^a=f^27,e^b=e^2,f^b=f^2,f^c=f^72,f^d=f^856 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 139);