Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #365×C167 ⋊ C2 |
| Sylow | C167 ⋊ #2231 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5344 |
Polycyclic presentation:
2^7,167|a^2=df,b^2=dg,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^b=h^166,e^c=efg,f^c=fg,h^c=h^1661351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 6685);