Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #475×C167 ⋊ C2 |
| Sylow | C167 ⋊ #3125 |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10688 |
Polycyclic presentation:
2^7,167|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^166,d^b=dg,h^b=h^166,f^c=fg,h^c=h^166,h^d=h^1661609 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 14794);