Finite Group DatabasebetaFinite Group Databasebeta| order | 1764 |
| isoclinism | isoclinic class of #64423 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#10596873 |
| derived, Sylow | C72 ⋊ C32×C4 |
| Hall | C3×#3861 ⋊ C4 |
| Hall | C7×Dic7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #64423 |
| commutator, hypocenter | C72 | C32×C4 |
| Frattini | C2 | C3×#64423 |
| Fitting, socle | C2×C3×C72 | C2×C3 |
| prime radical | C2×C3×#3861 | C2 |
| cosocle | C2×C72 | C2×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C3 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1764, 107);