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×#1410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | #353 |
| commutator | C42 | C2×C4×C127 |
| Frattini, cosocle | C4⋊Q8 | C22×C127 |
| prime radical | #127×C127 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ C4⋊Q8×C127 ◁ G | |
104 conjugacy classes of subgroups.
2159 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7517, C127×#7518, C127×#7527, … |
| maximal normal subgroup of | C127×#7517, C127×#7518, C127×#7527, … |
| maximal quotient of | C127×#7354, C127×#7371, C127×#7404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 142);