Finite Group DatabasebetaFinite Group Databasebeta| order | 1104 |
| isoclinism | isoclinic class of A4×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×A4×D23 |
| unambiguous semidirect product | C23⋊(C22×A4) |
| unambiguous semidirect product | (C2×C23)⋊(C2×A4) |
| unambiguous semidirect product | (C23×D23)⋊C3 |
| Fitting, socle | C23×C23 ⋊ C2×C3 |
| derived | C22×C23 ⋊ C22×C3 |
| Hall | C23×D23 ⋊ C3 |
| Sylow | C23 ⋊ C22×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×D23 |
| commutator, cosocle, hypocenter | C22×C23 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C23 | C2×C3 |
| LCS | G ▷ C22×C23 | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 138 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1104, 163);