Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C3×D3×C82 |
| Fitting | C32×C82 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C82 |
| Sylow | C32 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C82 | D3 |
| commutator, hypocenter | C3 | C2×C3×C82 |
| Frattini | C42 | C22×C3×D3 |
| Fitting | C32×C82 | C2 |
| socle | C22×C32 | C2×C42 |
| prime radical | C22×C3×D3 | C42 |
| cosocle | C3×C42 | C23×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C82 | |
597 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 597 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#1712, C3×D3×#1705, C3×D3×#1455, … |
| maximal normal subgroup of | C3×D3×#1712, C3×D3×#1705, C3×D3×#1455 |
| maximal quotient of | C82×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7503);