Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C3×C43 |
| direct product | C43×C3⋊D3 |
| Fitting | C32×C43 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C43 |
| Frattini | C23 | C23×C3⋊D3 |
| Fitting | C32×C43 | C2 |
| socle, cosocle | C23×C32 | C24 |
| prime radical | C23×C3⋊D3 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C43 | |
3816 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C3⋊D3×#97, C4×C3⋊D3×#127, C42×C3⋊D3×AGL(1,𝔽5), … |
| maximal normal subgroup of | C4×C3⋊D3×#97, C4×C3⋊D3×#127, C4×#10590393 |
| maximal quotient of | C4×C3⋊D3×#97, C42×C3⋊D3×AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34652);