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×C42 |
| direct product | #2500×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C131 |
| prime radical | C2×#121×C131 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8384 |
4978 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#9446, C131×#11550, C131×#11554, … |
| maximal normal subgroup of | C131×#9446, C131×#11550, C131×#11554, … |
| maximal quotient of | C131×#13879, C131×#13939, C131×#14001, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 1232);