Finite Group DatabasebetaFinite Group Databasebeta| order | 1104 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23 · Schur multiplier (H2) = C4 |
| direct product | C23×C42⋊C3 |
| unambiguous semidirect product | C42⋊(C3×C23) |
| unambiguous semidirect product | (C42×C23)⋊C3 |
| Fitting, Hall | C42×C23 ⋊ C3 |
| derived, Sylow | C42 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C42⋊C3 |
| commutator, cosocle, hypocenter | C42 | C3×C23 |
| Frattini | C22 | A4×C23 |
| Fitting | C42×C23 | C3 |
| socle | C22×C23 | A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C23 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1104, 30);