Finite Group DatabasebetaFinite Group Databasebeta| order | 8364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | D3×D17×C41 |
| unambiguous semidirect product | (D3×C17)⋊(C2×C41) |
| unambiguous semidirect product | (C3×D17)⋊(C2×C41) |
| unambiguous semidirect product | D51⋊(C2×C41) |
| Fitting, socle, Hall | C3×C17×C41 ⋊ C22 |
| derived, Hall | C3×C17 ⋊ C22×C41 |
| Hall | C17×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D3×C41 |
| Sylow | C3 ⋊ C2×D17×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D3×D17 |
| commutator, hypocenter | C3×C17 | C22×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C41 | C22 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C41 | |
40 conjugacy classes of subgroups.
1230 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D17×C41, C3×D3×D17×C41, D3×C41×D51, … |
| maximal normal subgroup of | C3×D3×D17×C41 |
| maximal quotient of | D9×D17×C41, C3×D3×D17×C41, D3×C41×D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8364, 25);