Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#430 |
758 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=e,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=hi,i^a=hi^2,c^b=cg,h^d=h^2,i^d=i^2,h^f=h^2,i^f=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 92652);