Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of ΓL(1,𝔽16)⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ΓL(1,𝔽16)⋊D11 |
| unambiguous semidirect product | D33⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C11⋊AGL(1,𝔽5))⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C11 ⋊ C2×C4 |
| Hall | C5×C11 ⋊ C4×D3 |
| Hall | C3×C11 ⋊ C2×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ C4×D11 |
| Sylow | C11 ⋊ D3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ D33⋊C4 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C11 | C2×C4 |
| prime radical | D5×D33 | C2 |
| cosocle | C3×D5×C11 | C22 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 165 |
Polycyclic presentation:
2^3,3,5,11|b^2=c,d^a=d^2,f^a=f^10,d^b=d^2,e^b=e^2,e^c=e^460 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×D11, #72245309 |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×D11, #72245309 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 152);