Finite Group DatabasebetaFinite Group Databasebeta| order | 5439 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C37 ⋊ C3 |
| Sylow | C72 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ #3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C37 | C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
3,7^2,37|b^a=b^2,c^a=c^2,d^a=d^26607 conjugacy classes — view the full character table.
| maximal subgroup of | #24925947, #24925949, #24925957, … |
| maximal normal subgroup of | #24925947, #24925949, #24925957, … |
| maximal quotient of | C2×#19129588, #30654570, C3×#19129588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5439, 12);