Finite Group DatabasebetaFinite Group Databasebeta| order | 984 |
| isoclinism | isoclinic class of A4×D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×D41 |
| unambiguous semidirect product | C41⋊(C2×A4) |
| unambiguous semidirect product | (C22×D41)⋊C3 |
| Fitting, socle, derived | C22×C41 ⋊ C2×C3 |
| Hall | C22×D41 ⋊ C3 |
| Sylow | C41 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C41 | C2×C3 |
| LCS | G ▷ C22×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 164 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | A4⋊#4223, A4×#4223, S4×D41, … |
| maximal normal subgroup of | A4⋊#4223, A4×#4223, S4×D41, … |
| maximal quotient of | C41⋊(#41⋊C3), SL(2,𝔽3)×D41, A4×Dic41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(984, 38);