Finite Group DatabasebetaFinite Group Databasebeta| order | 10812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D901 |
| unambiguous semidirect product | (D3×C17)⋊D53 |
| unambiguous semidirect product | (D3×C53)⋊D17 |
| Fitting, socle, derived, Hall | C3×C17×C53 ⋊ C22 |
| Hall | C17×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×D17 |
| Sylow | C53 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×D53 |
| Sylow | C17 ⋊ D3×D53 |
| Sylow | C3 ⋊ C2×D901 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C53 | C22 |
| LCS | G ▷ C3×C17×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1356 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D901, C3×D3×D901, D3×D2703, … |
| maximal normal subgroup of | C3×D3×D901 |
| maximal quotient of | D9×D901, C3×D3×D901, D3×D2703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10812, 27);