Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #491 |
270 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=f,c^2=e,d^2=f,b^a=be,c^a=cef,g^a=g^2,h^a=h^2,c^b=cd,d^b=df,d^c=df72 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#491, C2×#10592496, D3×#4797, … |
| maximal normal subgroup of | C3⋊D3×#491, C2×#10592496, D3×#4797, … |
| maximal quotient of | #11786062, #11789832, #11789835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4378);