Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C22⋊C8×C181 ⋊ C4 |
| Sylow | C181 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 124 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=e,e^2=g,b^a=bd,h^a=h^19,h^b=h^19,h^c=h^162,h^e=h^180,h^f=h^180980 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 20245);