Finite Group DatabasebetaFinite Group Databasebeta| order | 5526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D307 |
| Fitting, socle, Hall | C32×C307 ⋊ C2 |
| derived, Sylow | C307 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D307 |
| commutator, hypocenter | C307 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C307 | C2 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
1395 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D307, C3⋊D3×D307, C2×C32×D307, … |
| maximal normal subgroup of | C3×D3×D307, C3⋊D3×D307, C2×C32×D307, … |
| maximal quotient of | C32×Dic307, C2×C32×D307, C32×C5×D307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5526, 14);