Finite Group DatabasebetaFinite Group Databasebeta| order | 1104 |
| isoclinism | isoclinic class of S4×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | S4×D23 |
| unambiguous semidirect product | (C23×S4)⋊C2 |
| unambiguous semidirect product | (A4⋊D23)⋊C2 |
| unambiguous semidirect product | (A4×D23)⋊C2 |
| Fitting, socle | C22×C23 ⋊ C2×D3 |
| derived | A4×C23 ⋊ C22 |
| Sylow | C23 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C23 | C22 |
| Fitting, socle | C22×C23 | C2×D3 |
| LCS | G ▷ A4×C23 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 92 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | S4×AGL(1,𝔽23) |
| maximal normal subgroup of | S4×AGL(1,𝔽23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1104, 160);