Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C127 · Schur multiplier (H2) = C22×C8 |
| direct product | C127×#1712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C127 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C42×C127 ◁ G | |
280 conjugacy classes of subgroups.
4826 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7096, C127×#7529, C127×#12310, … |
| maximal normal subgroup of | C127×#7096, C127×#7529, C127×#12310, … |
| maximal quotient of | C127×#8818, C127×#9824, C127×#10304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 444);