Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4⋊C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #1646 |
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10688 |
Polycyclic presentation:
2^7,167|a^2=g,b^2=f,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^166,d^b=df,e^b=eg,h^b=h^166,d^c=dg,e^c=eg,h^c=h^1662350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 3741);