Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C167 ⋊ #2255 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21376 |
Polycyclic presentation:
2^7,167|a^2=d,b^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^166,c^b=cg3346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 6796);