Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×#24926260 |
| derived, Hall | C52×C109 ⋊ C3×C4 |
| Hall | C3×C52×C109 ⋊ C4 |
| Hall | C3×C109 ⋊ #1039 |
| Sylow | C109 ⋊ C3×#1039 |
| Hall | C3×C52 ⋊ Dic109 |
| Sylow | C52 ⋊ C3×Dic109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊D545 |
| commutator, hypocenter | C52×C109 | C3×C4 |
| Frattini | C2 | C3×C5⋊D545 |
| Fitting, socle, prime radical | C2×C3×C52×C109 | C2 |
| cosocle | C2×C52×C109 | C2×C3 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 ◁ C2×C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32700 |
8184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 76);