Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #456×C181 ⋊ C2 |
| Sylow | C181 ⋊ #3018 |
724 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2896 |
Polycyclic presentation:
2^7,181|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^180,e^b=eg,f^b=fg,e^c=eg,h^c=h^180,h^d=h^1801472 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 13862);