Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D2725 |
| unambiguous semidirect product | (D3×C25)⋊D109 |
| unambiguous semidirect product | (D3×C109)⋊D25 |
| Fitting, derived, Hall | C3×C25×C109 ⋊ C22 |
| Hall | C25×C109 ⋊ C2×D3 |
| Hall | C3×C109 ⋊ C2×D25 |
| Sylow | C109 ⋊ D3×D25 |
| Hall | C3×C25 ⋊ C2×D109 |
| Sylow | C25 ⋊ D3×D109 |
| Sylow | C3 ⋊ C2×D2725 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C25×C109 | C22 |
| Frattini | C5 | D3×D545 |
| socle | C3×C5×C109 | C2×D5 |
| LCS | G ▷ C3×C25×C109 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8175 |
4092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 41);