Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D165 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊#168) |
| unambiguous semidirect product | C11⋊(C3⋊#168) |
| derived, Hall | C3×C5×C11 ⋊ C8 |
| Hall | C5×C11 ⋊ C3⋊C8 |
| Hall | C3×C11 ⋊ #168 |
| Hall | C3×C5 ⋊ C11⋊C8 |
| Sylow | C11 ⋊ C3⋊#168 |
| Sylow | C5 ⋊ C3⋊(C11⋊C8) |
| Sylow | C3 ⋊ C11⋊#168 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D165 |
| commutator, hypocenter | C3×C5×C11 | C8 |
| Fitting, cosocle | C3×C4×C5×C11 | C2 |
| socle, prime radical | C2×C3×C5×C11 | C4 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 ◁ C4 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1320 |
Polycyclic presentation:
2^3,3,5,11|a^2=b,b^2=c,d^a=d^2,e^a=e^4,f^a=f^10336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 11);