Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C19×C49 ⋊ C2×C3 |
| Hall | #14584107 ⋊ C2 |
| Hall | C19×D49 ⋊ C3 |
| Hall | D49 ⋊ C19⋊C3 |
| Sylow | C49 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C19×C49 | C2×C3 |
| Frattini | C7 | #11716325 |
| socle | C7×C19 | AGL(1,𝔽7) |
| LCS | G ▷ C19×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,19,7|c^7=e^6,c^a=c^6e,e^a=e^6,c^b=c^2e^3,d^b=d^7,e^b=e^2170 conjugacy classes — view the full character table.
| maximal subgroup of | #19150251⋊C2, C2×#19150255, C19⋊C3×D49⋊C3, … |
| maximal normal subgroup of | #19150251⋊C2, C2×#19150255, C19⋊C3×D49⋊C3, … |
| maximal quotient of | #26013748, C2×#19150255, #30660483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 10);