Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16861628 |
| Sylow | C257 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
532 conjugacy classes — view the full character table.
| maximal subgroup of | #30657607, #30657613, #30657620, … |
| maximal normal subgroup of | #30657607, #30657613, #30657620, … |
| maximal quotient of | C2×#22551647, C4×#16861628, C2×#22551649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 232);