Finite Group DatabasebetaFinite Group Databasebeta| order | 8364 |
| isoclinism | isoclinic class of C3⋊#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C3⋊#4223 |
| unambiguous semidirect product | C3⋊(C17×#4223) |
| Fitting, socle, Hall | C3×C17×C41 ⋊ C4 |
| derived, Hall | C3×C41 ⋊ C4×C17 |
| Hall | C17×C41 ⋊ Dic3 |
| Hall | C3×C17 ⋊ #4223 |
| Sylow | C41 ⋊ Dic3×C17 |
| Sylow | C3 ⋊ C17×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊#4223 |
| commutator, hypocenter | C3×C41 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C41 | C4 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
612 conjugacy classes — view the full character table.
| maximal subgroup of | C17×C9⋊#4223, C3×C17×C3⋊#4223, C17×C3⋊(C3⋊#4223) |
| maximal normal subgroup of | C3×C17×C3⋊#4223 |
| maximal quotient of | C17×C9⋊#4223, C3×C17×C3⋊#4223, C17×C3⋊(C3⋊#4223) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8364, 17);