Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C53 |
| direct product | C4×C532⋊C3 |
| unambiguous semidirect product | (C4×C532)⋊C3 |
| Fitting, Hall | C4×C532 ⋊ C3 |
| derived, Sylow | C532 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C532⋊C3 |
| commutator, hypocenter | C532 | C3×C4 |
| Frattini | C2 | C2×C532⋊C3 |
| Fitting | C4×C532 | C3 |
| socle, cosocle | C2×C532 | C2×C3 |
| prime radical | C2×C532⋊C3 | C2 |
| LCS | G ▷ C532 | |
| UCS | C1 ◁ C4 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 636 |
3756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 16);