Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #379×C127 ⋊ C2 |
| Sylow | C127 ⋊ #2405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D127 |
| commutator, socle, cosocle | C23×C127 | C24 |
| Fitting | #379×C127 | C2 |
| prime radical | C23×C22⋊D127 | C2 |
| hypercenter | #379 | D127 |
| hypocenter | C127 | #2405 |
| LCS | G ▷ C23×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ #379 | |
1116 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,127|c^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^126,h^d=h^1261802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 7835);