Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D257 |
| unambiguous semidirect product | C257⋊C25 |
| unambiguous semidirect product | (C2×C257)⋊C24 |
| Fitting, socle | C24×C257 ⋊ C2 |
| derived, Sylow | C257 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D257 |
| commutator, hypocenter | C257 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C257 | C2 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656592, C2×C22⋊C4×D257, C22×#16861595, … |
| maximal normal subgroup of | #30656592, C2×C22⋊C4×D257, C22×#16861595, … |
| maximal quotient of | C23×C4×D257, C24×Dic257, C22×D4×D257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 195);