Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C24×C4 |
| direct product | #2684×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C131 |
| prime radical | C2×#120×C131 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
688 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4192 |
4192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#13348, C131×#13424, C131×#36702, … |
| maximal normal subgroup of | C131×#13348, C131×#13424, C131×#36702, … |
| maximal quotient of | C131×#14357, C131×#14365, C131×#14393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 1416);