Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic545 |
| derived | C5×C109 ⋊ C3×C4×C5 |
| Hall | C3×C52×C109 ⋊ C4 |
| Hall | C52×C109 ⋊ C3×C4 |
| Hall | C3×C109 ⋊ C5×Dic5 |
| Sylow | C109 ⋊ C3×C5×Dic5 |
| Hall | C3×C52 ⋊ Dic109 |
| Sylow | C52 ⋊ C3×Dic109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D545 |
| commutator, hypocenter | C5×C109 | C3×C4×C5 |
| Frattini | C2 | C3×C5×D545 |
| Fitting, socle, prime radical | C2×C3×C52×C109 | C2 |
| cosocle | C2×C5×C109 | C2×C3×C5 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 ◁ C2×C3×C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6540 |
8220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 78);