Finite Group DatabasebetaFinite Group Databasebeta| order | 32100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C107 · Schur multiplier (H2) = C2 |
| direct product | D5×D15×C107 |
| unambiguous semidirect product | (C3×D5)⋊(D5×C107) |
| unambiguous semidirect product | (C5×D5)⋊(D3×C107) |
| Fitting, socle, Hall | C3×C52×C107 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C22×C107 |
| Hall | C52×C107 ⋊ C2×D3 |
| Hall | C3×C107 ⋊ D52 |
| Sylow | C52 ⋊ C2×D3×C107 |
| Sylow | C3 ⋊ D52×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | D5×D15 |
| commutator, cosocle, hypocenter | C3×C52 | C22×C107 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C107 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C107 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3210 |
3852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32100, 85);