Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×C49×#261 |
| Fitting, Hall | C3×C13×C49 ⋊ C4 |
| derived, Sylow | C13 ⋊ C3×C4×C49 |
| Hall | C13×C49 ⋊ C3×C4 |
| Hall | C3×C13 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C49 | #261 |
| commutator, hypocenter | C13 | C3×C4×C49 |
| Frattini | C7 | C3×C7×#261 |
| Fitting | C3×C13×C49 | C4 |
| socle | C3×C7×C13 | C4×C7 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C49 | |
36 conjugacy classes of subgroups.
1029 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×#261⋊C9, #261×C49⋊C9, #37524084, … |
| maximal normal subgroup of | C49×#261⋊C9, #261×C49⋊C9, #37524084, … |
| maximal quotient of | C9×C49×#261, C32×C49×#261, C3×C49×C3⋊#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 50);