Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C9⋊C16 |
| derived, Sylow | C9 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D9 |
| commutator, hypocenter | C9 | C2×C4×C16 |
| Frattini | C2×C3×C8 | C22×D3 |
| Fitting | C2×C4×C8×C9 | C2 |
| socle, prime radical | C23×C3 | C2×C3⋊C8 |
| cosocle | C2×C8×C9 | C23 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C4×C8 | |
324 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, 29816);