Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C22×H(5,𝔽2) ⋊ C9 |
2273 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 2273 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3^2,2^5|a^2=i,b^2=i,c^3=d,e^2=i,f^2=i,b^a=bi,e^c=ef,f^c=e,g^c=gh,h^c=g,f^e=fi108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153908);