Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic637 |
| derived, Hall | C13×C49 ⋊ C3×C4 |
| Hall | C3×C13×C49 ⋊ C4 |
| Hall | C3×C49 ⋊ Dic13 |
| Sylow | C49 ⋊ C3×Dic13 |
| Hall | C3×C13 ⋊ Dic49 |
| Sylow | C13 ⋊ C3×Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D637 |
| commutator, hypocenter | C13×C49 | C3×C4 |
| Frattini | C2×C7 | C3×D91 |
| Fitting | C2×C3×C13×C49 | C2 |
| socle | C2×C3×C7×C13 | D7 |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
1920 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37524059, (C49⋊C9)⋊Dic13, #37524067, … |
| maximal normal subgroup of | #37524059, (C49⋊C9)⋊Dic13, #37524067, … |
| maximal quotient of | C9×Dic637, C32×Dic637, C3×Dic1911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 20);