Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #3363 |
542 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,i^a=hi^2,d^b=de,h^b=h^2,i^b=i^2,f^c=fg,h^c=hi,i^c=i^2,h^f=h^2,i^f=i^263 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 129514);