Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C32 |
No aliases for this group.
| derived | C3×H(3,𝔽3) ⋊ C3×C4 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C4 |
319 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,d^a=d^2,e^a=e^2,f^a=f^2,d^b=df,e^d=eg78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 329);