Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ #518 |
742 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|d^2=e,c^a=cf,h^a=h^2,c^b=cf,d^b=df,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #11788864, D3×#5545, #11900010, … |
| maximal normal subgroup of | #11788864, D3×#5545, #11900010, … |
| maximal quotient of | #11800859, #11800864, #11800881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6138);