Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #3359 |
1110 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 321 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,i^a=i^2,d^b=de,f^c=fg135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 129165);