Finite Group DatabasebetaFinite Group Databasebeta| order | 984 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×A4×C41 |
| unambiguous semidirect product | C23⋊(C3×C41) |
| unambiguous semidirect product | (C23×C41)⋊C3 |
| Fitting, socle, Hall | C23×C41 ⋊ C3 |
| derived | C22 ⋊ C2×C3×C41 |
| Sylow | C23 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | A4 |
| commutator, cosocle, hypocenter | C22 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C23×C41 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C41 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 246 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×SL(2,ℤ/4), A4⋊Dic41, A4×Dic41, … |
| maximal normal subgroup of | C41×SL(2,ℤ/4), A4⋊Dic41, A4×Dic41, … |
| maximal quotient of | C4×A4×C41, C2×SL(2,𝔽3)×C41, C41×#41⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(984, 42);