Finite Group DatabasebetaFinite Group Databasebeta| order | 10812 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C3×C53×#595 |
| Fitting, socle, Hall | C3×C17×C53 ⋊ C4 |
| derived, Sylow | C17 ⋊ C3×C4×C53 |
| Hall | C17×C53 ⋊ C3×C4 |
| Hall | C3×C17 ⋊ C4×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C53 | #595 |
| commutator, hypocenter | C17 | C3×C4×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C53 | C4 |
| prime radical | C3×D17×C53 | C2 |
| cosocle | D17 | C2×C3×C53 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C3×C53 | |
24 conjugacy classes of subgroups.
1272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C53×#595, C32×C53×#595, C3×C53×C3⋊#595 |
| maximal normal subgroup of | C9×C53×#595, C32×C53×#595 |
| maximal quotient of | C9×C53×#595, C32×C53×#595, C3×C53×C3⋊#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10812, 11);