Finite Group DatabasebetaFinite Group Databasebeta| order | 5644 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic83 |
| unambiguous semidirect product | C83⋊(C4×C17) |
| derived, Sylow | C83 ⋊ C4×C17 |
| Hall | C17×C83 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D83 |
| commutator, hypocenter | C83 | C4×C17 |
| Frattini | C2 | C17×D83 |
| Fitting, socle | C2×C17×C83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C2×C17 | |
12 conjugacy classes of subgroups.
1462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×Dic83, C17×Dic249, C5×C17×Dic83, … |
| maximal normal subgroup of | C3×C17×Dic83, C5×C17×Dic83 |
| maximal quotient of | C3×C17×Dic83, C17×Dic249, C5×C17×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5644, 3);