Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×#89137⋊C3 |
| unambiguous semidirect product | #89137⋊(C3×C52) |
| unambiguous semidirect product | (C5×#89137)⋊(C3×C5) |
| Fitting, socle, Hall | C52×C109 ⋊ C3×C4 |
| derived, Sylow | C109 ⋊ C3×C4×C52 |
| Hall | C52×#89137 ⋊ C3 |
| Hall | C52×C109⋊C3 ⋊ C4 |
| Hall | #89137 ⋊ C3×C52 |
| Hall | C109⋊C3 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | #89137⋊C3 |
| commutator, hypocenter | C109 | C3×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C109 | C3×C4 |
| prime radical | C52×D109⋊C3 | C2 |
| cosocle | D109 | C2×C3×C52 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2725 |
525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 104);