Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C181 ⋊ C2 |
| Sylow | C181 ⋊ #3019 |
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^180,e^b=eg,f^b=fg,e^c=eg3089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 13867);