Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C11⋊C5)⋊C8) |
| unambiguous semidirect product | (C11⋊C5)⋊(C3⋊C8) |
| unambiguous semidirect product | (C3⋊(C11⋊C8))⋊C5 |
| derived, Hall | C3×C11 ⋊ C5×C8 |
| Hall | C3⋊(C11⋊C8) ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C8 |
| Hall | C11⋊C5 ⋊ C3⋊C8 |
| Sylow | C11 ⋊ C5×C3⋊C8 |
| Sylow | C3 ⋊ (C11⋊C5)⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C3⋊AGL(1,𝔽11) |
| commutator, hypocenter | C3×C11 | C5×C8 |
| Fitting, cosocle | C3×C4×C11 | C2×C5 |
| socle | C2×C3×C11 | C4×C5 |
| prime radical | C2×C3×C11⋊C5 | C4 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C4 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2,5,2^2,3,11|a^2=c,c^2=d,e^a=e^2,f^a=f^10,f^b=f^972 conjugacy classes — view the full character table.
| maximal subgroup of | C8×C3⋊AGL(1,𝔽11), #72216768, D3×(C11⋊C5)⋊C8, … |
| maximal normal subgroup of | C8×C3⋊AGL(1,𝔽11), #72216768, D3×(C11⋊C5)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 3);