Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#24926271 |
| Fitting, socle, Hall | C3×C52×C109 ⋊ C4 |
| derived, Hall | C52×C109 ⋊ C3×C4 |
| Hall | C3×C109 ⋊ #1043 |
| Sylow | C109 ⋊ C3×#1043 |
| Hall | C3×C52 ⋊ #89137 |
| Sylow | C52 ⋊ C3×#89137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #24926271 |
| commutator, hypocenter | C52×C109 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C109 | C4 |
| prime radical | C3×C5⋊D545 | C2 |
| cosocle | C5⋊D545 | C2×C3 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8175 |
2055 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 158);