Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C127 ⋊ #2295 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D127 |
| commutator | C22×C127 | C23×C4 |
| Fitting | #387×C127 | C2 |
| socle, prime radical, cosocle | C23×C127 | C24 |
| hypercenter | #387 | D127 |
| hypocenter | C127 | #2295 |
| LCS | G ▷ C22×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ #387 | |
500 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,127|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^c=h^126,h^d=h^1261820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 6983);