Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10587722⋊D7 |
| Fitting, socle, derived, Hall | C72×C13 ⋊ C22×C3 |
| Hall | (C7⋊D7)⋊D13 ⋊ C3 |
| Hall | C7×#63270 ⋊ C22 |
| Sylow | C72 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ D7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C22×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7^2,13|d^a=d^6,f^a=f^12,d^b=d^6,e^b=e^6,d^c=d^2,f^c=f^387 conjugacy classes — view the full character table.
| maximal subgroup of | #37524922, #37524928, #37524929, … |
| maximal normal subgroup of | #37524922, #37524928, #37524929, … |
| maximal quotient of | #13109902⋊D7, C3×#10587722⋊D7, #37525203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 209);