Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | #4296⋊#5997 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C4×C9 |
| Hall | C72×#4296 ⋊ C4 |
| Hall | C19⋊#5997 ⋊ C9 |
| Hall | #4296 ⋊ #5997 |
| Sylow | C72 ⋊ #4296⋊C4 |
| Sylow | C19 ⋊ C9×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C4×C9 |
| prime radical, cosocle | C19⋊C3×C7⋊D7 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2,3,2,3,7^2,19|a^2=c,b^3=d,e^a=e^3f^5,f^a=e^5f^4,g^a=g^18,g^b=g^4,e^c=e^6,f^c=f^6,g^d=g^7170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 775);