Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C127 · Schur multiplier (H2) = C24 |
| direct product | C127×#3195 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C127 |
| prime radical | C24×C127 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G | |
410 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3302 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#9342, C127×#9935, C127×#9937, … |
| maximal normal subgroup of | C127×#9342, C127×#9935, C127×#9937, … |
| maximal quotient of | C127×#21765, C127×#21942 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 1927);