Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C13 ⋊ C22×C3 |
| Hall | D7×D91 ⋊ C3 |
| Hall | C13⋊#3862 ⋊ C22 |
| Sylow | C72 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ #64422⋊C2 |
| 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|e^a=e^6,f^a=f^12,d^b=d^6,d^c=d^2,e^c=e^4,f^c=f^989 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#10587722, #37524921, #37524927, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#10587722, #37524921, #37524927, … |
| maximal quotient of | #37524433, C3×#21439618, #37525346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 187);