Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C53 |
| unambiguous semidirect product | C3⋊#26014496 |
| derived, Hall | C3×C532 ⋊ C4 |
| Sylow | C532 ⋊ Dic3 |
| Sylow | C3 ⋊ #26014496 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C53⋊D53) |
| commutator, hypocenter | C3×C532 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C532 | C2 |
| LCS | G ▷ C3×C532 | |
| UCS | C1 ◁ C2 | |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33708 |
Polycyclic presentation:
2,3,53^2,2|a^2=e,b^a=b^2,c^a=c^52,d^a=d^528430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 17);