Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11759967 |
| unambiguous semidirect product | D257⋊C42 |
| Fitting | C2×C4×C257 ⋊ C4 |
| derived, Sylow | C257 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11759967 |
| commutator, hypocenter | C257 | C2×C42 |
| Frattini | C2 | C22×#11759967 |
| Fitting | C2×C4×C257 | C4 |
| socle | C22×C257 | C2×C4 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | #30657602, #30657607, #30657609, … |
| maximal normal subgroup of | #30657602, #30657607, #30657609, … |
| maximal quotient of | C42×#11759967, C2×(C2×#11759967)⋊C4, #30657673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 222);