Finite Group DatabasebetaFinite Group Databasebeta| order | 30906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1717 |
| unambiguous semidirect product | C17⋊(C32×D101) |
| unambiguous semidirect product | C101⋊(C32×D17) |
| Fitting, socle, Hall | C32×C17×C101 ⋊ C2 |
| derived, Hall | C17×C101 ⋊ C2×C32 |
| Hall | C32×C101 ⋊ D17 |
| Hall | C32×C17 ⋊ D101 |
| Sylow | C101 ⋊ C32×D17 |
| Sylow | C17 ⋊ C32×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1717 |
| commutator, cosocle, hypocenter | C17×C101 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C101 | C2 |
| LCS | G ▷ C17×C101 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15453 |
7740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30906, 12);