Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C28 |
| direct product | C2×#386×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C131 | C23 |
| commutator | C22 | C23×C4×C131 |
| Frattini, cosocle | C23 | C24×C131 |
| prime radical | C23×D4×C131 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C131 ◁ G | |
1576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8384 |
7336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#9079, C131×#9083, C131×#10745, … |
| maximal normal subgroup of | C131×#9079, C131×#9083, C131×#10745, … |
| maximal quotient of | C2×C22⋊#95×C131, C2×#1436×C131, C2×#1437×C131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 1019);