Finite Group DatabasebetaFinite Group Databasebeta| order | 17612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#14578980 |
| Fitting, socle, derived, Hall | C7×C17×C37 ⋊ C4 |
| Hall | C17×C37 ⋊ Dic7 |
| Hall | C7×C37 ⋊ #595 |
| Hall | C7×C17 ⋊ #3866 |
| Sylow | C37 ⋊ C7⋊#595 |
| Sylow | C17 ⋊ C7⋊#3866 |
| Sylow | C7 ⋊ #14578980 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C17×C37 | C4 |
| prime radical, cosocle | C7×D629 | C2 |
| LCS | G ▷ C7×C17×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4403 |
Polycyclic presentation:
2^2,7,17,37|a^2=b,c^a=c^6,d^a=d^13,e^a=e^6,d^b=d^16,e^b=e^361109 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17612, 21);