Finite Group DatabasebetaFinite Group Databasebeta| order | 10812 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×#6157 |
| Fitting, socle, Hall | C3×C17×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C3×C4×C17 |
| Hall | C17×C53 ⋊ C3×C4 |
| Hall | C3×C53 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | #6157 |
| commutator, hypocenter | C53 | C3×C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C53 | C4 |
| prime radical | C3×C17×D53 | C2 |
| cosocle | D53 | C2×C3×C17 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C3×C17 | |
24 conjugacy classes of subgroups.
867 conjugacy classes — view the full character table.
| maximal subgroup of | C9×C17×#6157, C32×C17×#6157, C3×C17×C3⋊#6157 |
| maximal normal subgroup of | C9×C17×#6157, C32×C17×#6157 |
| maximal quotient of | C9×C17×#6157, C32×C17×#6157, C3×C17×C3⋊#6157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10812, 10);