Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×#103 ⋊ C2 |
| Sylow | C32 ⋊ #452 |
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=ef,c^2=f,d^2=f,b^a=be,c^a=cf,g^a=g^2,h^a=h^2,c^b=cd,d^b=df,d^c=df75 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#452, C2×#10592507, D3×#4808, … |
| maximal normal subgroup of | C3⋊D3×#452, C2×#10592507, D3×#4808, … |
| maximal quotient of | #11778286, #11778399, #11778738, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4389);