Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D257 |
| Fitting | C16×C257 ⋊ C2 |
| derived, Sylow | C257 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D257 |
| commutator, hypocenter | C257 | C2×C16 |
| Frattini | C8 | C2×D257 |
| Fitting | C16×C257 | C2 |
| socle | C2×C257 | C2×C8 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C16 | |
28 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D257, #30656570, C2×C16×D257, … |
| maximal normal subgroup of | C32×D257, #30656570, C2×C16×D257, … |
| maximal quotient of | C16×Dic257, #30656516, #30656555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 83);