Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C127 · Schur multiplier (H2) = C25 |
| direct product | C127×#2931 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C127 | C23 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C2×C4 | C24×C127 |
| socle | C22×C127 | C23×C4 |
| prime radical | #532×C127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C127 ◁ G | |
500 conjugacy classes of subgroups.
7112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#8241, C127×#8243, C127×#8245, … |
| maximal normal subgroup of | C127×#8241, C127×#8243, C127×#8245, … |
| maximal quotient of | C127×#17956, C127×#17957, C127×#17958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1663);