Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D257 |
| Fitting | C2×Q8×C257 ⋊ C2 |
| Sylow | C257 ⋊ C22×Q8 |
| 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 | C22×Q8 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
156 conjugacy classes of subgroups.
1300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D257, #103×D257, #30656744, … |
| maximal normal subgroup of | #101×D257, #103×D257, #30656744, … |
| maximal quotient of | C2×C4⋊C4×D257, C4×Q8×D257, C2×#22551557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 185);