Finite Group DatabasebetaFinite Group Databasebeta| order | 17612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C37 · Schur multiplier (H2) = C2 |
| direct product | D7×D17×C37 |
| unambiguous semidirect product | (D7×C17)⋊(C2×C37) |
| unambiguous semidirect product | (C7×D17)⋊(C2×C37) |
| unambiguous semidirect product | D119⋊(C2×C37) |
| Fitting, socle, Hall | C7×C17×C37 ⋊ C22 |
| derived, Hall | C7×C17 ⋊ C22×C37 |
| Hall | C17×C37 ⋊ C2×D7 |
| Hall | C7×C37 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D7×C37 |
| Sylow | C7 ⋊ C2×D17×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D7×D17 |
| commutator, cosocle, hypocenter | C7×C17 | C22×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C37 | C22 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C37 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4403 |
1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17612, 25);