Finite Group DatabasebetaFinite Group Databasebeta| order | 1992 |
| isoclinism | isoclinic class of A4⋊D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A4⋊D83 |
| unambiguous semidirect product | C83⋊S4 |
| Fitting, socle | C22×C83 ⋊ D3 |
| derived | A4×C83 ⋊ C2 |
| Sylow | C83 ⋊ S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C83 | C2 |
| Fitting, socle | C22×C83 | D3 |
| LCS | G ▷ A4×C83 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 332 |
Polycyclic presentation:
2,3,83,2^2|b^a=b^2,c^a=c^82,d^a=de,d^b=e,e^b=de169 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1992, 32);