Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×(C7⋊D7)⋊D13 |
| Fitting, socle, Hall | C3×C72×C13 ⋊ C22 |
| derived, Hall | C72×C13 ⋊ C22×C3 |
| Hall | C3×C72 ⋊ C2×D13 |
| Sylow | C72 ⋊ C2×C3×D13 |
| Hall | C3×C13 ⋊ D72 |
| Sylow | C13 ⋊ C3×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C7⋊D7)⋊D13 |
| commutator, hypocenter | C72×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C22 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
104 conjugacy classes of subgroups.
543 conjugacy classes — view the full character table.
| maximal subgroup of | #37524425, #37524426, #11725077⋊D13, … |
| maximal normal subgroup of | #37524425, #37524426, #11725077⋊D13, … |
| maximal quotient of | C9×(C7⋊D7)⋊D13, C32×(C7⋊D7)⋊D13, C3×D91⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 320);