Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of C3⋊(C11⋊AGL(1,𝔽5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(C11⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | (C2×C3)⋊(C11⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | D5⋊Dic33 |
| unambiguous semidirect product | (C2×C11)⋊ΓL(1,𝔽16) |
| Fitting, socle | C2×C3×C5×C11 ⋊ C4 |
| derived, Hall | C3×C5×C11 ⋊ C2×C4 |
| Hall | C5×C11 ⋊ C2×Dic3 |
| Hall | C3×C11 ⋊ C2×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ C2×Dic11 |
| Sylow | C11 ⋊ C2×ΓL(1,𝔽16) |
| Sylow | C5 ⋊ C2×Dic33 |
| Sylow | C3 ⋊ C2×C11⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C11⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C3×C5×C11 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C11 | C4 |
| prime radical | C2×C3×D5×C11 | C2 |
| cosocle | C3×D5×C11 | C22 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 165);