Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | D3×C72×D13 |
| unambiguous semidirect product | (D3×C13)⋊(C2×C72) |
| unambiguous semidirect product | (C3×D13)⋊(C2×C72) |
| unambiguous semidirect product | D39⋊(C2×C72) |
| Fitting, socle, Hall | C3×C72×C13 ⋊ C22 |
| derived, Hall | C3×C13 ⋊ C22×C72 |
| Hall | C72×C13 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D3×C72 |
| Sylow | C3 ⋊ C2×C72×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D3×D13 |
| commutator, hypocenter | C3×C13 | C22×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C72 | |
200 conjugacy classes of subgroups.
1176 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×D9×D13, D3×C72×D13⋊C3, D3×C7×#10587716, … |
| maximal normal subgroup of | D3×C72×D13⋊C3, D3×C7×#10587716, D3×C7×#10587717, … |
| maximal quotient of | C72×D9×D13, C3×D3×C72×D13, D3×C72×D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 325);