Finite Group DatabasebetaFinite Group Databasebeta| order | 32820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5×D547 |
| Fitting, socle | C2×C3×C5×C547 ⋊ C2 |
| derived, Sylow | C547 ⋊ C22×C3×C5 |
| Hall | C3×C5×C547 ⋊ C22 |
| Hall | C5×C547 ⋊ C22×C3 |
| Hall | C3×C547 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D547 |
| commutator, cosocle, hypocenter | C547 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C547 | C2 |
| LCS | G ▷ C547 | |
| UCS | C1 ◁ C2×C3×C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16410 |
8250 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32820, 34);