Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊#3874) |
| Fitting, socle, Hall | C52×C112 ⋊ D3 |
| derived, Hall | C112×C52⋊C3 ⋊ C2 |
| Sylow | C112 ⋊ #3874 |
| Hall | C52⋊C3 ⋊ C11⋊D11 |
| Sylow | C52 ⋊ C3⋊(C11⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C112×C52⋊C3 | C2 |
| Fitting, socle | C52×C112 | D3 |
| LCS | G ▷ C112×C52⋊C3 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1815 |
Polycyclic presentation:
2,3,11^2,5^2|b^a=b^2,c^a=c^10,d^a=d^10,e^a=e^2f,f^a=e^2f^3,e^b=e^2f^4,f^b=e^2f^2673 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C11⋊#3874, #3874×C11⋊D11, #49137581, … |
| maximal normal subgroup of | D11×C11⋊#3874, #3874×C11⋊D11, #49137581, … |
| maximal quotient of | C11⋊(C11⋊#64470), C2×C11⋊(C11⋊#3874) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 171);