Finite Group DatabasebetaFinite Group Databasebeta| order | 984 |
| isoclinism | isoclinic class of S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C2 |
| direct product | S4×C41 |
| unambiguous semidirect product | A4⋊(C2×C41) |
| Fitting, socle | C22×C41 ⋊ D3 |
| derived | A4 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | S4 |
| commutator, cosocle, hypocenter | A4 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C22×C41 | D3 |
| LCS | G ▷ A4 | |
| UCS | C1 ◁ C41 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 164 |
205 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D41, C2×S4×C41, S4×C41⋊C5 |
| maximal normal subgroup of | S4×D41, C2×S4×C41, S4×C41⋊C5 |
| maximal quotient of | C41×#226, C41×GL(2,𝔽3), C41×SL(2,ℤ/4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(984, 36);