Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C109 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C109×C3⋊(C5⋊D5) |
| unambiguous semidirect product | (C2×C3)⋊(C5⋊D5×C109) |
| unambiguous semidirect product | (C2×C5)⋊(D15×C109) |
| Fitting, socle | C2×C3×C52×C109 ⋊ C2 |
| derived, Hall | C3×C52 ⋊ C22×C109 |
| Hall | C3×C52×C109 ⋊ C22 |
| Hall | C52×C109 ⋊ C2×D3 |
| Hall | C3×C109 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D3×C109 |
| Sylow | C3 ⋊ C2×C5⋊D5×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C109 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C22×C109 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C109 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2×C109 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16350 |
8502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 215);