Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C127 · Schur multiplier (H2) = C2×C4 |
| direct product | C127×#2248 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C127 |
| prime radical | #493×C127 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C42×C127 ◁ C4×C8×C127 ◁ G | |
196 conjugacy classes of subgroups.
4826 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#12318, C127×#12319, C127×#12320, … |
| maximal normal subgroup of | C127×#12318, C127×#12319, C127×#12320, … |
| maximal quotient of | C127×#12505, C127×#12509, C127×#12510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 980);