Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26013821 |
| derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×C19×#3861 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C3×#3861 ⋊ Dic19 |
| Sylow | C72 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ C3⋊#10596874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#19150288 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C19×#3861 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11172 |
Polycyclic presentation:
2,3^2,7^2,19,2|a^2=g,c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^18,d^b=d^2,e^b=e^21092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 705);