Finite Group DatabasebetaFinite Group Databasebeta| order | 5439 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C37⋊#3862 |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C3 |
| Sylow | C72 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ #3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C37 | C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3,7^2,37|b^a=b^2,c^a=c^4,d^a=d^26607 conjugacy classes — view the full character table.
| maximal subgroup of | #24925953, #24925954, #24925963, … |
| maximal normal subgroup of | #24925953, #24925954, #24925963, … |
| maximal quotient of | C2×C37⋊#3862, #30654573, C3×C37⋊#3862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5439, 15);