Finite Group DatabasebetaFinite Group Databasebeta| order | 33550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C2×C5×#16809824 |
| Fitting, socle | C2×C5×C11×C61 ⋊ C5 |
| derived, Hall | C11×C61 ⋊ C2×C52 |
| Hall | C2×C11×C61 ⋊ C52 |
| Hall | C2×C61 ⋊ C5×C11⋊C5 |
| Sylow | C61 ⋊ C2×C5×C11⋊C5 |
| Hall | C2×C11 ⋊ C5×C61⋊C5 |
| Sylow | C11 ⋊ C2×C5×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #16809824 |
| commutator, cosocle, hypocenter | C11×C61 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C61 | C5 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C2×C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6710 |
1390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33550, 82);