Finite Group DatabasebetaFinite Group Databasebeta| order | 33460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic239⋊C7 |
| unambiguous semidirect product | Dic239⋊(C5×C7) |
| unambiguous semidirect product | (C239⋊C7)⋊(C4×C5) |
| unambiguous semidirect product | (C5×Dic239)⋊C7 |
| derived, Sylow | C239 ⋊ C4×C5×C7 |
| Hall | C5×C239⋊C7 ⋊ C4 |
| Hall | C5×Dic239 ⋊ C7 |
| Hall | C239⋊C7 ⋊ C4×C5 |
| Hall | C5×C239 ⋊ C4×C7 |
| Hall | Dic239 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D239⋊C7 |
| commutator, hypocenter | C239 | C4×C5×C7 |
| Frattini | C2 | C5×D239⋊C7 |
| Fitting, socle | C2×C5×C239 | C2×C7 |
| prime radical | C2×C5×C239⋊C7 | C2 |
| cosocle | C2×C239 | C2×C5×C7 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4780 |
310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33460, 10);