Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C127 · Schur multiplier (H2) = C24 |
| direct product | C127×#2000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C127 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C127 |
| prime radical | C2×#121×C127 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G | |
444 conjugacy classes of subgroups.
4064 conjugacy classes. The character table is too large to display.
| maximal quotient of | C127×#9916, C127×#9917, C127×#9920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 732);