Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #117×C79 ⋊ C2 |
| Sylow | C79 ⋊ #421 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D316 |
| commutator | C4×C79 | C22×C4 |
| Frattini | C2×C4 | C22×D79 |
| Fitting | #117×C79 | C2 |
| socle | C2×C79 | C2×C22⋊C4 |
| hypercenter | #117 | D79 |
| hypocenter | C79 | #421 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #117 | |
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^78,c^b=cf,d^b=df,g^b=g^78802 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 567);