Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×SL(2,𝔽3) |
| unambiguous semidirect product | Q8⋊(C3×C5×C11) |
| unambiguous semidirect product | (C5×Q8)⋊(C3×C11) |
| unambiguous semidirect product | (C5×Q8×C11)⋊C3 |
| Fitting, Hall | C5×Q8×C11 ⋊ C3 |
| derived, Sylow | Q8 ⋊ C3×C5×C11 |
| Hall | Q8×C11 ⋊ C3×C5 |
| Hall | C5×Q8 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C5×C11 | A4 |
| commutator, cosocle, hypocenter | Q8 | C3×C5×C11 |
| Frattini | C2 | C5×C11×A4 |
| Fitting | C5×Q8×C11 | C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C5×C11 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 94);