Finite Group DatabasebetaFinite Group Databasebeta| order | 5216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic163 |
| Sylow | C163 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D163 |
| commutator | C2×C163 | C22×C4 |
| Fitting | C2×Q8×C163 | C2 |
| socle | C22×C163 | C23 |
| hypercenter | C2×Q8 | D163 |
| hypocenter | C163 | C4×Q8 |
| LCS | G ▷ C2×C163 ▷ C163 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
70 conjugacy classes of subgroups.
830 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5216, 113);