Finite Group DatabasebetaFinite Group Databasebeta| order | 5412 |
| automorphism | Aut(G) order 2164800 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2706 |
| direct product | C2×D1353 |
| unambiguous semidirect product | (C2×C3)⋊D451 |
| unambiguous semidirect product | (C2×C11)⋊D123 |
| unambiguous semidirect product | (C2×C41)⋊D33 |
| Fitting, socle | C2×C3×C11×C41 ⋊ C2 |
| derived, Hall | C3×C11×C41 ⋊ C22 |
| Hall | C11×C41 ⋊ C2×D3 |
| Hall | C3×C41 ⋊ C2×D11 |
| Sylow | C41 ⋊ C2×D33 |
| Hall | C3×C11 ⋊ C2×D41 |
| Sylow | C11 ⋊ C2×D123 |
| Sylow | C3 ⋊ C2×D451 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1353 |
| commutator, hypocenter | C3×C11×C41 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C11×C41 | C2 |
| LCS | G ▷ C3×C11×C41 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1356 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4059, D3×D1353, C2×C3⋊D1353, … |
| maximal normal subgroup of | C2×C3×D1353, C2×C3⋊#17985247, C2×C3⋊#17985250, … |
| maximal quotient of | C2×D4059, D3×D1353, C2×C3⋊D1353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5412, 22);