Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16861619 |
| Fitting | C2×Q8×C257 ⋊ C2 |
| Sylow | C257 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D257 |
| commutator | C2×C257 | C24 |
| Frattini | C2 | C23×D257 |
| Fitting | C2×Q8×C257 | C2 |
| socle | C22×C257 | C23 |
| hypercenter | C2×Q8 | D257 |
| hypocenter | C257 | C2×#41 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
164 conjugacy classes of subgroups.
1300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656720, #30656732, #30656737, … |
| maximal normal subgroup of | #30656720, #30656732, #30656737, … |
| maximal quotient of | C2×#22551550, C2×#22551554, C2×Q8×Dic257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 190);