Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #568×C167 ⋊ C2 |
| Sylow | C167 ⋊ #1914 |
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2672 |
Polycyclic presentation:
2^7,167|a^2=f,b^2=df,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^166,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg2851 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 5057);