Finite Group DatabasebetaFinite Group Databasebeta| order | 10804 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×#3866 |
| Fitting, socle, Hall | C37×C73 ⋊ C4 |
| derived, Sylow | C37 ⋊ C4×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | #3866 |
| commutator, hypocenter | C37 | C4×C73 |
| Frattini | C1 | G |
| Fitting, socle | C37×C73 | C4 |
| prime radical | C73×D37 | C2 |
| cosocle | D37 | C2×C73 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C73 | |
12 conjugacy classes of subgroups.
949 conjugacy classes — view the full character table.
| maximal subgroup of | C73×#3866⋊C3, #44569433, #44569434, … |
| maximal normal subgroup of | C73×#3866⋊C3, #44569433, #44569434, … |
| maximal quotient of | C3×C73×#3866, C73×C3⋊#3866 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10804, 7);