Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C3 · Schur multiplier (H2) = C221 |
| direct product | C26×C3×D3 |
| unambiguous semidirect product | C3⋊(C27×C3) |
| unambiguous semidirect product | (C2×C3)⋊(C26×C3) |
| Fitting, socle | C26×C32 ⋊ C2 |
| derived | C3 ⋊ C27×C3 |
| Sylow | C32 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26×C3 | D3 |
| commutator, cosocle, hypocenter | C3 | C27×C3 |
| Frattini | C1 | G |
| Fitting, socle | C26×C32 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C26×C3 | |
119673 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153311);