Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C25 |
| direct product | #2315×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C24 |
| commutator | C22 | C23×C4×C131 |
| Frattini, cosocle | C23 | C24×C131 |
| prime radical | C25×C131 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
816 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4192 |
5764 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#8756, C131×#8853, C131×#8854, … |
| maximal normal subgroup of | C131×#8756, C131×#8853, C131×#8854, … |
| maximal quotient of | C131×#13778, C131×#13782, C131×#13794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 1047);