Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C127 · Schur multiplier (H2) = C4 |
| direct product | C127×#1406 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | #353 |
| commutator | C42 | C2×C4×C127 |
| Frattini, cosocle | #124 | C22×C127 |
| prime radical | #496×C127 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ #124×C127 ◁ G | |
108 conjugacy classes of subgroups.
1778 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C127×#1406, C127×#13577, C127×#13578, … |
| maximal normal subgroup of | C2×C127×#1406, C127×#13577, C127×#13578, … |
| maximal quotient of | C127×#7352, C127×#7372, C127×#7402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 138);