Finite Group DatabasebetaFinite Group Databasebeta| order | 30906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C101 · Schur multiplier (H2) = C3 |
| direct product | C101×C3⋊D51 |
| unambiguous semidirect product | C3⋊(C101×D51) |
| unambiguous semidirect product | C17⋊(C3⋊D3×C101) |
| Fitting, socle, Hall | C32×C17×C101 ⋊ C2 |
| derived, Hall | C32×C17 ⋊ C2×C101 |
| Hall | C17×C101 ⋊ C3⋊D3 |
| Hall | C32×C101 ⋊ D17 |
| Sylow | C17 ⋊ C3⋊D3×C101 |
| Sylow | C32 ⋊ D17×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | C3⋊D51 |
| commutator, cosocle, hypocenter | C32×C17 | C2×C101 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C101 | C2 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C101 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15453 |
7878 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30906, 19);