Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C22×C4 |
| direct product | #2607×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C131 |
| prime radical | C24×C131 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
444 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8384 |
4978 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#10386, C131×#10387, C131×#12121, … |
| maximal normal subgroup of | C131×#10386, C131×#10387, C131×#12121, … |
| maximal quotient of | C131×#13953, C131×#14091, C131×#14093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 1339);