Finite Group DatabasebetaFinite Group Databasebeta| order | 5216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C163 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D163 |
| commutator | C2×C163 | C22×C4 |
| Frattini | C22 | C22×D163 |
| Fitting | C22×C4×C163 | C2 |
| socle | C22×C163 | C23 |
| hypercenter | C22×C4 | D163 |
| hypocenter | C163 | #117 |
| LCS | G ▷ C2×C163 ▷ C163 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,163|a^2=e,c^2=d,b^a=bd,f^a=f^1621316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5216, 105);