Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #344 |
270 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=f,b^a=be,d^a=df,g^a=g^2,h^a=h^2,e^b=ef102 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#344, C2×#10589399, D3×#4533, … |
| maximal normal subgroup of | C3⋊D3×#344, C2×#10589399, D3×#4533, … |
| maximal quotient of | #11770818, #11770838, #11770852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1281);