Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #494×C167 ⋊ C2 |
| Sylow | C167 ⋊ #2248 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10688 |
Polycyclic presentation:
2^7,167|b^2=dfg,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^166,h^b=h^1661864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 6767);