Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C8×C181 ⋊ C4 |
| Sylow | C181 ⋊ #1746 |
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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,b^2=f,c^2=d,e^2=g,b^a=bd,c^b=cg,h^b=h^162,h^f=h^1801496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 20228);