Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C3×C42×Dic3 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C43) |
| derived | C3 ⋊ C2×C3×C43 |
| Sylow | C32 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C42 | D3 |
| commutator, hypocenter | C3 | C2×C3×C43 |
| Frattini | C23 | C23×C3×D3 |
| Fitting | C22×C32×C42 | C2 |
| socle, prime radical | C24×C32 | C23 |
| cosocle | C23×C3 | C24×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C3×C42 | |
2793 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34656);