Finite Group DatabasebetaFinite Group Databasebeta| order | 5439 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C37×C49 ⋊ C3 |
| Sylow | C49 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C37×C49 | C3 |
| Frattini | C7 | #11715913 |
| socle | C7×C37 | ΓL(1,𝔽8) |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,37,7|b^7=d^4,b^a=b^4d,c^a=c^10,d^a=d^4607 conjugacy classes — view the full character table.
| maximal subgroup of | #24925914, #24925918, #24925920, … |
| maximal normal subgroup of | #24925914, #24925918, #24925920, … |
| maximal quotient of | C2×#19129581, #30654554, C3×#19129581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5439, 5);