Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| isoclinism | isoclinic class of C22⋊(C19⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C47 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C19×C47 ⋊ C3 |
| derived, Hall | C22×C19 ⋊ C3×C47 |
| Hall | C19×C47 ⋊ A4 |
| Hall | C22×C47 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ A4×C47 |
| Sylow | C22 ⋊ C47×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C22⋊(C19⋊C3) |
| commutator, cosocle, hypocenter | C22×C19 | C3×C47 |
| Frattini | C1 | G |
| Fitting, socle | C22×C19×C47 | C3 |
| LCS | G ▷ C22×C19 | |
| UCS | C1 ◁ C47 | |
20 conjugacy classes of subgroups.
1316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C47×C19⋊C3, C3×C47×C22⋊(C19⋊C3) |
| maximal normal subgroup of | A4×C47×C19⋊C3, C3×C47×C22⋊(C19⋊C3) |
| maximal quotient of | C47×C22⋊#4294, C3×C47×C22⋊(C19⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 25);