Finite Group DatabasebetaFinite Group Databasebeta| order | 5072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C317 ⋊ C2 |
| Sylow | C317 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D317 |
| commutator, socle | C2×C317 | C23 |
| Frattini | C2 | C22×D317 |
| Fitting | C2×C4×C317 | C2 |
| hypercenter | C2×C4 | D317 |
| hypocenter | C317 | #41 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,317|c^2=d,b^a=bd,e^b=e^3161274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5072, 40);