Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×Dic57 |
| unambiguous semidirect product | C3⋊(C47×Dic19) |
| unambiguous semidirect product | C19⋊(Dic3×C47) |
| derived, Hall | C3×C19 ⋊ C4×C47 |
| Hall | C3×C19×C47 ⋊ C4 |
| Hall | C19×C47 ⋊ Dic3 |
| Hall | C3×C47 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic3×C47 |
| Sylow | C3 ⋊ C47×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D57 |
| commutator, hypocenter | C3×C19 | C4×C47 |
| Frattini | C2 | C47×D57 |
| Fitting, socle, prime radical | C2×C3×C19×C47 | C2 |
| cosocle | C2×C3×C19 | C2×C47 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C47 | |
24 conjugacy classes of subgroups.
2820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×Dic171, C47×C3⋊((C19⋊C3)⋊C4), C47×C3⋊Dic57, … |
| maximal normal subgroup of | C47×C3⋊((C19⋊C3)⋊C4), C3×C47×Dic57 |
| maximal quotient of | C47×Dic171, C47×C3⋊Dic57, C3×C47×Dic57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 8);