Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52×C109 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×A4×C109 |
| unambiguous semidirect product | C22⋊(C3×C52×C109) |
| unambiguous semidirect product | (C22×C5)⋊(C3×C5×C109) |
| Fitting, socle, Hall | C22×C52×C109 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C52×C109 |
| Hall | C22×C109 ⋊ C3×C52 |
| Hall | C22×C52 ⋊ C3×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C109 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C52×C109 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C109 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C52×C109 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10900 |
10900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 201);