Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #2875 |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10688 |
Polycyclic presentation:
2^7,167|a^2=e,b^2=f,e^2=g,b^a=bg,h^a=h^166,d^c=dg,h^d=h^1663388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 12939);