Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D25×D109 |
| Fitting, Hall | C3×C25×C109 ⋊ C22 |
| derived, Hall | C25×C109 ⋊ C22×C3 |
| Hall | C3×C109 ⋊ C2×D25 |
| Sylow | C109 ⋊ C2×C3×D25 |
| Hall | C3×C25 ⋊ C2×D109 |
| Sylow | C25 ⋊ C2×C3×D109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×D109 |
| commutator, cosocle, hypocenter | C25×C109 | C22×C3 |
| Frattini | C5 | C3×D5×D109 |
| Fitting | C3×C25×C109 | C22 |
| socle | C3×C5×C109 | C2×D5 |
| LCS | G ▷ C25×C109 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8175 |
2352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 30);