Finite Group DatabasebetaFinite Group Databasebeta| order | 5612 |
| automorphism | Aut(G) order 3703920 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2806 |
| direct product | C2×D1403 |
| unambiguous semidirect product | (C2×C23)⋊D61 |
| unambiguous semidirect product | (C2×C61)⋊D23 |
| Fitting, socle | C2×C23×C61 ⋊ C2 |
| derived, Hall | C23×C61 ⋊ C22 |
| Sylow | C61 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1403 |
| commutator, hypocenter | C23×C61 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C61 | C2 |
| LCS | G ▷ C23×C61 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23⋊(D61⋊C3), D3×D1403, C2×D4209, … |
| maximal normal subgroup of | C2×C23⋊(D61⋊C3), C2×C3×D1403, C2×C23⋊(D61⋊C5), … |
| maximal quotient of | D3×D1403, C2×D4209, C2×C3×D1403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5612, 9);