Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C127 · Schur multiplier (H2) = C1 |
| direct product | C127×#1338 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | C22⋊C4 |
| commutator | C2×C4 | C2×C8×C127 |
| Frattini, cosocle | C4×C8 | C22×C127 |
| socle, prime radical | C22×C127 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ G | |
86 conjugacy classes of subgroups.
4826 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C127×#1338, C127×#11610, C127×#11611, … |
| maximal normal subgroup of | C2×C127×#1338, C127×#11610, C127×#11611, … |
| maximal quotient of | C127×#7118, C127×#7128, C127×#7170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 70);