Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×D257 |
| Fitting | C22×C4×C257 ⋊ C2 |
| derived, Sylow | C257 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D257 |
| commutator, hypocenter | C257 | C23×C4 |
| Frattini | C2 | C23×D257 |
| Fitting | C22×C4×C257 | C2 |
| socle | C23×C257 | C22 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×D257, #30656584, C4×#16861595, … |
| maximal normal subgroup of | #95×D257, #30656584, C4×#16861595, … |
| maximal quotient of | C2×C42×D257, C22×C4×Dic257, C2×C22⋊C4×D257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 180);