Finite Group DatabasebetaFinite Group Databasebeta| order | 33370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D47×C71⋊C5 |
| unambiguous semidirect product | C47⋊(C2×C71⋊C5) |
| unambiguous semidirect product | (C71×D47)⋊C5 |
| Fitting, socle, derived, Hall | C47×C71 ⋊ C2×C5 |
| Hall | C47×C71⋊C5 ⋊ C2 |
| Hall | C71×D47 ⋊ C5 |
| Sylow | C71 ⋊ C5×D47 |
| Sylow | C47 ⋊ C2×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C71 | C2×C5 |
| LCS | G ▷ C47×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3337 |
475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33370, 11);