Finite Group DatabasebetaFinite Group Databasebeta| order | 5244 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic69 |
| unambiguous semidirect product | C3⋊(C19×Dic23) |
| unambiguous semidirect product | C23⋊(Dic3×C19) |
| derived, Hall | C3×C23 ⋊ C4×C19 |
| Hall | C3×C19×C23 ⋊ C4 |
| Hall | C19×C23 ⋊ Dic3 |
| Hall | C3×C19 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic3×C19 |
| Sylow | C3 ⋊ C19×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D69 |
| commutator, hypocenter | C3×C23 | C4×C19 |
| Frattini | C2 | C19×D69 |
| Fitting, socle | C2×C3×C19×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C19 | |
24 conjugacy classes of subgroups.
1368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×Dic207, C19⋊C3×Dic69, C3×C19×Dic69, … |
| maximal normal subgroup of | C19⋊C3×Dic69, C3×C19×Dic69, C5×C19×Dic69, … |
| maximal quotient of | C19×Dic207, C3×C19×Dic69, C19×C3⋊Dic69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5244, 7);