Finite Group DatabasebetaFinite Group Databasebeta| order | 33550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C61 · Schur multiplier (H2) = C1 |
| direct product | D5×C11⋊C5×C61 |
| unambiguous semidirect product | C5⋊(C2×C11⋊C5×C61) |
| unambiguous semidirect product | (D5×C11)⋊(C5×C61) |
| Fitting, socle | C5×C11×C61 ⋊ C2×C5 |
| derived | C5×C11 ⋊ C2×C5×C61 |
| Hall | C5×C11⋊C5×C61 ⋊ C2 |
| Hall | C11×C61 ⋊ C5×D5 |
| Hall | C5×C11⋊C5 ⋊ C2×C61 |
| Sylow | C11 ⋊ C5×D5×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D5×C11⋊C5 |
| commutator, cosocle, hypocenter | C5×C11 | C2×C5×C61 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C61 | C2×C5 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C61 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3355 |
1708 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33550, 68);