Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C181 ⋊ #1603 |
244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=eg,d^c=dg,h^c=h^1801733 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 3470);