Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #1294 |
494 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=efg,i^a=hi^2,c^b=cg,h^b=hi,i^b=hi^2,h^c=h^2,i^c=i^2,h^e=h^2,i^e=i^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5067);