Finite Group DatabasebetaFinite Group Databasebeta| order | 11550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊D385) |
| unambiguous semidirect product | C5⋊D1155 |
| unambiguous semidirect product | C7⋊(C3⋊(C5⋊D55)) |
| unambiguous semidirect product | C11⋊(C3⋊(C5⋊D35)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C7×C11 | C2 |
| LCS | G ▷ C3×C52×C7×C11 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7,11|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^102889 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1155, D55×D105, D35×D165, … |
| maximal normal subgroup of | D5×D1155, D55×D105, D35×D165, … |
| maximal quotient of | C3⋊(C7⋊(C11⋊#1039)), C2×C3⋊(C5⋊D385), C5⋊D3465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11550, 94);