Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D79 |
| commutator, socle | C2×C79 | C23×C4 |
| Fitting | C2×M16×C79 | C2 |
| hypercenter | C2×M16 | D79 |
| hypocenter | C79 | #568 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,79|a^2=e,e^2=f,d^a=df,c^b=cf,g^c=g^78814 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 1315);