Finite Group DatabasebetaFinite Group Databasebeta| order | 8364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D51 |
| unambiguous semidirect product | (C3×D41)⋊D17 |
| unambiguous semidirect product | (C17×D41)⋊D3 |
| Fitting, socle, derived, Hall | C3×C17×C41 ⋊ C22 |
| Hall | C17×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D51 |
| Sylow | C17 ⋊ D3×D41 |
| Sylow | C3 ⋊ D17×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C41 | C22 |
| LCS | G ▷ C3×C17×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
594 conjugacy classes — view the full character table.
| maximal subgroup of | D41×D153, C3×D41×D51, D123⋊D51, … |
| maximal normal subgroup of | C3×D41×D51 |
| maximal quotient of | D41×D153, C3×D41×D51, D123⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8364, 24);