Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 193536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C32×C127 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C23×C127 |
| socle, prime radical | C23×C127 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
16256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7465, C127×#7470, C127×#7471, … |
| maximal normal subgroup of | C127×#7465, C127×#7470, C127×#7471, … |
| maximal quotient of | C2×C4×C32×C127, C2×C127×C22⋊C32, C2×C127×C4⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 988);