Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #357×C181 ⋊ C2 |
| Sylow | C181 ⋊ #2140 |
260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=e,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=df,f^b=fg,h^c=h^1802012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 6224);