Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊((C19⋊C3)⋊#5997) |
| unambiguous semidirect product | (C19⋊C3)⋊(C3⋊#5997) |
| Fitting, socle, derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×C72×C19⋊C3 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ #5997 |
| Sylow | C72 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3×C3⋊#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C19 | C3×C4 |
| prime radical | C3×C19⋊C3×C7⋊D7 | C2 |
| cosocle | C3×C19×C7⋊D7 | C2×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
Polycyclic presentation:
2,3,2,3,7^2,19|a^2=c,d^a=d^2,e^a=e^4f^3,f^a=e^6f^3,g^a=g^18,g^b=g^7,e^c=e^6,f^c=f^6360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 1060);