Finite Group DatabasebetaFinite Group Databasebeta| order | 8364 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#14584035 |
| Fitting, socle, Hall | C3×C17×C41 ⋊ C4 |
| derived, Hall | C17×C41 ⋊ C3×C4 |
| Hall | C3×C41 ⋊ Dic17 |
| Hall | C3×C17 ⋊ #4223 |
| Sylow | C41 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ C3×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14584035 |
| commutator, hypocenter | C17×C41 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C41 | C4 |
| LCS | G ▷ C17×C41 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
570 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#14584035, C32×#14584035, C3×C3⋊#14584035 |
| maximal normal subgroup of | C9×#14584035, C32×#14584035 |
| maximal quotient of | C9×#14584035, C32×#14584035, C3×C3⋊#14584035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8364, 15);