Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C16×C181 ⋊ C2 |
| Sylow | C181 ⋊ #1360 |
102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11584 |
Polycyclic presentation:
2^7,181|a^2=d,c^2=fg,d^2=ef,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^180,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^1803629 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 2554);