Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20259503 |
| Fitting, socle, derived | C3×C7×C73 ⋊ C3×C4 |
| Hall | C3×#13095276 ⋊ C4 |
| Hall | C7×C73 ⋊ C3×Dic3 |
| Sylow | C73 ⋊ Dic3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3⋊(#64408⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C73 | C3×C4 |
| prime radical | C3×#15690442 | C2 |
| cosocle | C3×C7×D73 | C2×C3 |
| LCS | G ▷ C3×C7×C73 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1533 |
Polycyclic presentation:
2,3,2,3,7,73|a^2=c,d^a=d^2,f^a=f^27,e^b=e^2,f^b=f^64,f^c=f^72156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 195);