Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C32 ⋊ C4×#107 |
474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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=e,b^2=f,c^2=deg,d^2=g,e^2=g,b^a=bd,h^a=hi,i^a=hi^2,d^b=dg,e^b=eg,i^b=hi^2,h^c=h^2,i^c=i^2,h^d=h^2,i^d=i^2,h^e=h^2,i^e=i^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18489);