Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| derived | C3×SL(2,𝔽3) ⋊ C42 |
460 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 93 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:
2^4,3^2,2^3|a^2=d,b^2=c,g^2=i,h^2=i,b^a=bi,e^a=e^2,f^a=f^2,g^a=gh,h^a=hi,g^e=h,h^e=ghi,h^g=hi108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155029);