Finite Group DatabasebetaFinite Group Databasebeta| order | 33417 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×C79⋊C9 |
| unambiguous semidirect product | C79⋊(C9×C47) |
| unambiguous semidirect product | (C47×C79)⋊C9 |
| derived, Sylow | C79 ⋊ C9×C47 |
| Hall | C47×C79 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C47 | C79⋊C3 |
| commutator, hypocenter | C79 | C9×C47 |
| Frattini | C3 | C47×C79⋊C3 |
| Fitting, socle, prime radical | C3×C47×C79 | C3 |
| cosocle | C3×C79 | C3×C47 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3×C47 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33417 |
4089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33417, 2);