Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C53 |
| unambiguous semidirect product | C3⋊#26014502 |
| Fitting, socle, derived, Hall | C3×C532 ⋊ C4 |
| Sylow | C532 ⋊ Dic3 |
| Sylow | C3 ⋊ #26014502 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C532 | C4 |
| prime radical, cosocle | C3×C53⋊D53 | C2 |
| LCS | G ▷ C3×C532 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 318 |
Polycyclic presentation:
2^2,3,53^2|a^2=b,c^a=c^2,d^a=d^30,e^a=e^23,d^b=d^52,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, 40);