Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊#4294 |
| derived, Hall | C52×C19 ⋊ C2×C9 |
| Hall | C52⋊#4294 ⋊ C2 |
| Hall | C19×C5⋊D5 ⋊ C9 |
| Hall | C5⋊D5 ⋊ #4294 |
| Sylow | C52 ⋊ C2×#4294 |
| Sylow | C19 ⋊ (C5⋊D5)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C5⋊D5)⋊(C19⋊C3) |
| 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,c^b=cd^3,d^b=c^4d^3,e^b=e^7282 conjugacy classes — view the full character table.
| maximal subgroup of | #30685552, #1043⋊#4294, #22555508⋊C2, … |
| maximal normal subgroup of | #30685552, #1043⋊#4294, #22555508⋊C2, … |
| maximal quotient of | #1039⋊#4294, C2×(C5⋊D5)⋊#4294 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 47);