Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | #41×H(3,𝔽3) ⋊ C3 |
| Sylow | #41 ⋊ #732 |
135 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^4,2^3|a^2=h,f^2=h,g^2=h,c^b=cd,d^b=de,f^b=fg,g^b=f,d^c=de,g^f=gh90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 990);