Finite Group DatabasebetaFinite Group Databasebeta| order | 7548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#14578981 |
| Fitting, socle, derived, Hall | C3×C17×C37 ⋊ C4 |
| Hall | C17×C37 ⋊ Dic3 |
| Hall | C3×C37 ⋊ #595 |
| Hall | C3×C17 ⋊ Dic37 |
| Sylow | C37 ⋊ C3⋊#595 |
| Sylow | C17 ⋊ Dic111 |
| Sylow | C3 ⋊ #14578981 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C37 | C4 |
| LCS | G ▷ C3×C17×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,37|a^2=b,c^a=c^2,d^a=d^13,e^a=e^36,d^b=d^16558 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7548, 36);