Finite Group DatabasebetaFinite Group Databasebeta| order | 5216 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic163 |
| derived, Sylow | C163 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D163 |
| commutator, hypocenter | C163 | C4×C8 |
| Frattini | C2×C4 | C2×D163 |
| Fitting | C2×C8×C163 | C2 |
| socle | C22×C163 | C2×C4 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C2×C8 | |
44 conjugacy classes of subgroups.
1328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5216, 54);