Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #461×C151 ⋊ C2 |
| Sylow | C151 ⋊ #3303 |
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9664 |
Polycyclic presentation:
2^7,151|a^2=eg,b^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^150,d^b=de,h^b=h^150,f^c=fg,h^c=h^150,h^d=h^1501460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 16441);