Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26014492 |
| Fitting, derived, Hall | C3×C2809 ⋊ C4 |
| Sylow | C2809 ⋊ Dic3 |
| Sylow | C3 ⋊ #26014492 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C2809 | C4 |
| Frattini | C53 | C3⋊#6157 |
| socle | C3×C53 | #6157 |
| prime radical, cosocle | C3×D2809 | C2 |
| LCS | G ▷ C3×C2809 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8427 |
Polycyclic presentation:
2^2,3,53^2|a^2=b,d^53=e^6,c^a=c^2,d^a=d^23e,e^a=e^23,d^b=d^52e^47,e^b=e^522112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 7);