Finite Group DatabasebetaFinite Group Databasebeta| order | 10812 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16813360 |
| Fitting, socle, Hall | C3×C17×C53 ⋊ C4 |
| derived, Hall | C17×C53 ⋊ C3×C4 |
| Hall | C3×C53 ⋊ Dic17 |
| Sylow | C53 ⋊ C3×Dic17 |
| Hall | C3×C17 ⋊ #6157 |
| Sylow | C17 ⋊ C3×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16813360 |
| commutator, hypocenter | C17×C53 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C53 | C4 |
| prime radical | C3×C17×D53 | C2 |
| cosocle | C17×D53 | C2×C3 |
| LCS | G ▷ C17×C53 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
723 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16813360, C32×#16813360, C3×C3⋊#16813360 |
| maximal normal subgroup of | C9×#16813360, C32×#16813360 |
| maximal quotient of | C9×#16813360, C32×#16813360, C3×C3⋊#16813360 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10812, 15);