Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C149 ⋊ #2995 |
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9536 |
Polycyclic presentation:
2^7,149|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^105,c^b=ceg,d^b=dg,h^c=h^148,h^d=h^148,h^f=h^148556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 21466);