Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #343×C181 ⋊ C2 |
| Sylow | C181 ⋊ #1345 |
168 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 35 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=d,c^2=f,d^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cf,d^b=def,h^b=h^180,d^c=dg2003 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 2512);