Finite Group DatabasebetaFinite Group Databasebeta| order | 5452 |
| isoclinism | isoclinic class of D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×Dic47 |
| unambiguous semidirect product | C47⋊(C4×C29) |
| derived, Sylow | C47 ⋊ C4×C29 |
| Hall | C29×C47 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D47 |
| commutator, hypocenter | C47 | C4×C29 |
| Frattini | C2 | C29×D47 |
| Fitting, socle | C2×C29×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C29 | |
12 conjugacy classes of subgroups.
1450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C29×Dic47, C29×Dic141, C5×C29×Dic47, … |
| maximal normal subgroup of | C3×C29×Dic47, C5×C29×Dic47, C7×C29×Dic47, … |
| maximal quotient of | C3×C29×Dic47, C29×Dic141, C5×C29×Dic47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5452, 3);