Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C3×C7⋊D91 |
| Fitting, socle | C2×C3×C72×C13 ⋊ C2 |
| derived, Hall | C72×C13 ⋊ C22×C3 |
| Hall | C3×C72×C13 ⋊ C22 |
| Hall | C3×C72 ⋊ C2×D13 |
| Sylow | C72 ⋊ C2×C3×D13 |
| Hall | C3×C13 ⋊ C2×C7⋊D7 |
| Sylow | C13 ⋊ C2×C3×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C7⋊D91 |
| commutator, hypocenter | C72×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72×C13 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2×C3 | |
200 conjugacy classes of subgroups.
1920 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#26039444, C2×#26039445, C2×#26039448, … |
| maximal normal subgroup of | C2×#26039444, C2×#26039445, C2×#26039448, … |
| maximal quotient of | C2×C9×C7⋊D91, C3×D3×C7⋊D91, C2×C32×C7⋊D91, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 373);