Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C127 · Schur multiplier (H2) = C4 |
| direct product | C127×#1411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | #353 |
| commutator | C42 | C2×C4×C127 |
| Frattini, cosocle | C4⋊Q8 | C22×C127 |
| prime radical | C22×C127 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ C4⋊Q8×C127 ◁ G | |
94 conjugacy classes of subgroups.
2159 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7521, C127×#7522, C127×#7531, … |
| maximal normal subgroup of | C127×#7521, C127×#7522, C127×#7531, … |
| maximal quotient of | C127×#7355, C127×#7370, C127×#7405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 143);