Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M64×C167 ⋊ C2 |
| Sylow | C167 ⋊ #1418 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5344 |
Polycyclic presentation:
2^7,167|a^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^166,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^1663346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 2698);