Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×C9⋊C8 |
| derived, Sylow | C9 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D9 |
| commutator, hypocenter | C9 | C42×C8 |
| Frattini | C22×C3×C4 | C22×D3 |
| Fitting | C43×C9 | C2 |
| socle, prime radical | C23×C3 | C22×Dic3 |
| cosocle | C22×C4×C9 | C23 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C43 | |
612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17018);