Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C47 ⋊ #21802 |
1194 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,47|a^2=g,b^2=e,c^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=ce,d^b=dh,i^b=i^46,g^c=gh,i^c=i^46782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 178867);