Finite Group DatabasebetaFinite Group Databasebeta| order | 1452 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic33 |
| unambiguous semidirect product | C3⋊(C11×Dic11) |
| unambiguous semidirect product | C11⋊(C11×Dic3) |
| derived | C3×C11 ⋊ C4×C11 |
| Hall | C3×C112 ⋊ C4 |
| Sylow | C112 ⋊ Dic3 |
| Sylow | C3 ⋊ C11×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D33 |
| commutator, hypocenter | C3×C11 | C4×C11 |
| Frattini | C2 | C11×D33 |
| Fitting, socle, prime radical | C2×C3×C112 | C2 |
| cosocle | C2×C3×C11 | C2×C11 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C11 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17983705, C11×Dic99, C3⋊#13089712, … |
| maximal normal subgroup of | C3×C11×Dic33, C11×C13×Dic33, C11×C17×Dic33, … |
| maximal quotient of | C11×Dic99, C3×C11×Dic33, C11×C3⋊Dic33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1452, 17);