Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊#14579331 |
| Fitting, socle, derived, Hall | C3×C72×C13 ⋊ C4 |
| Hall | C72×C13 ⋊ Dic3 |
| Hall | C3×C72 ⋊ Dic13 |
| Sylow | C72 ⋊ Dic39 |
| Hall | C3×C13 ⋊ #5997 |
| Sylow | C13 ⋊ C3⋊#5997 |
| Sylow | C3 ⋊ #14579331 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C13 | C4 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7^2,13|a^2=b,c^a=c^2,d^a=d^4e^6,e^a=d^3e^3,f^a=f^12,d^b=d^6,e^b=e^6510 conjugacy classes — view the full character table.
| maximal subgroup of | #37524491, C9⋊#14579331, C3⋊#21439676, … |
| maximal normal subgroup of | C3⋊#21439687, C3⋊#21439680, C3⋊#21439681, … |
| maximal quotient of | C9⋊#14579331, C3×C3⋊#14579331, C3⋊(C3⋊#14579331), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 347);