Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×Dic9 |
| unambiguous semidirect product | (C2×C9)⋊C43 |
| derived, Sylow | C9 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D9 |
| commutator, hypocenter | C9 | C2×C43 |
| Frattini | C23×C3 | C23×D3 |
| Fitting | C22×C42×C9 | C2 |
| socle, prime radical | C24×C3 | C22×D3 |
| cosocle | C23×C9 | C24 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C42 | |
1908 conjugacy classes of subgroups; only the 1134 normal subgroups are shown.
This group has 1908 conjugacy classes of subgroups — too many to draw. Only its 1134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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, 34654);