Finite Group DatabasebetaFinite Group Databasebeta| order | 17612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D119⋊D37 |
| unambiguous semidirect product | D259⋊D17 |
| unambiguous semidirect product | D629⋊D7 |
| Fitting, socle, derived, Hall | C7×C17×C37 ⋊ C22 |
| Hall | C17×C37 ⋊ C2×D7 |
| Hall | C7×C37 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D37 |
| Sylow | C37 ⋊ D7×D17 |
| Sylow | C17 ⋊ D7×D37 |
| Sylow | C7 ⋊ D17×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C17×C37 | C22 |
| LCS | G ▷ C7×C17×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4403 |
Polycyclic presentation:
2^2,7,17,37|d^a=d^16,e^a=e^36,c^b=c^6,d^b=d^161148 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17612, 28);