Finite Group DatabasebetaFinite Group Databasebeta| order | 6188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D13×D17 |
| unambiguous semidirect product | (C17×D13)⋊(C2×C7) |
| unambiguous semidirect product | (C13×D17)⋊(C2×C7) |
| unambiguous semidirect product | D221⋊(C2×C7) |
| Fitting, socle, Hall | C7×C13×C17 ⋊ C22 |
| derived, Hall | C13×C17 ⋊ C22×C7 |
| Hall | C7×C17 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C7×D13 |
| Sylow | C13 ⋊ C2×C7×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D13×D17 |
| commutator, hypocenter | C13×C17 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C17 | C22 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D17×D13⋊C3, D17×#10587716, D17×#10587717, … |
| maximal normal subgroup of | C7×D17×D13⋊C3, D17×#10587716, D17×#10587717, … |
| maximal quotient of | C3×C7×D13×D17, C7×D17×D39, C7×D13×D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6188, 16);