Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C32×C4 |
| Hall | C19⋊C3×#3861 ⋊ C4 |
| Hall | C19⋊#5997 ⋊ C32 |
| Sylow | C72 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C3×#5997⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C32×C4 |
| prime radical | C19⋊C3×#64424 | C2 |
| cosocle | C19×C7⋊D7 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2,3^2,2,7^2,19|a^2=d,e^a=e^3f^5,f^a=e^5f^4,g^a=g^18,g^b=g^7,e^c=e^2,f^c=f^2,e^d=e^6,f^d=f^690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 784);