Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C22×C32×C9 ⋊ C22 |
| Sylow | C32×C9 ⋊ C2×D4 |
742 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^4,3^4|g^3=h,c^a=cd,e^a=e^2,f^a=f^2,c^b=cd,g^b=g^2h^2,h^b=h^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#88668, #72259402, #72259553, … |
| maximal normal subgroup of | D3×#88668, #72259553, D4×D9×C3⋊D3, … |
| maximal quotient of | #72259402, C2×#13048710 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2428);