Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C3×C72×C13 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D13 |
| Sylow | C72 ⋊ C2×D39 |
| Hall | C3×C13 ⋊ D72 |
| Sylow | C13 ⋊ D21⋊D7 |
| Sylow | C3 ⋊ (C7⋊D7)⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C13 | C22 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7^2,13|c^a=c^2,d^a=d^6,f^a=f^12,d^b=d^6,e^b=e^6519 conjugacy classes — view the full character table.
| maximal subgroup of | #37524486, #37524589, #37525130, … |
| maximal normal subgroup of | #37525222, #37525223, (ΓL(1,𝔽8)⋊D7)⋊D39, … |
| maximal quotient of | #37524589, C3×#21439774, #37525618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 343);