Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C26×D9 |
| unambiguous semidirect product | C9⋊C27 |
| unambiguous semidirect product | (C2×C9)⋊C26 |
| Fitting | C26×C9 ⋊ C2 |
| derived, Sylow | C9 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D9 |
| commutator, cosocle, hypocenter | C9 | C27 |
| Frattini | C3 | C26×D3 |
| Fitting | C26×C9 | C2 |
| socle | C26×C3 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C26 | |
87636 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×#2846, C22×D9×#120 |
| maximal normal subgroup of | D9×#2846, C22×D9×#120 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153309);