Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C52×C19 ⋊ C2×C9 |
| Hall | C52⋊#4294 ⋊ C2 |
| Hall | C5⋊D95 ⋊ C9 |
| Sylow | C52 ⋊ #4294⋊C2 |
| Sylow | C19 ⋊ (C5⋊D5)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15668133 |
| commutator, hypocenter | C52×C19 | C2×C9 |
| Fitting, socle | C3×C52×C19 | C2×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,19,3|b^3=f,c^a=c^4,d^a=d^4,e^a=e^18,c^b=cd,d^b=c^2d^3,e^b=e^7255 conjugacy classes — view the full character table.
| maximal subgroup of | #22555508⋊C2, C2×#22555508 |
| maximal normal subgroup of | #22555508⋊C2, C2×#22555508 |
| maximal quotient of | #30685437, C2×#22555508 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 46);