Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #367 |
110 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=ce,c^2=e,e^2=f,b^a=bc,c^a=cef,e^a=ef,h^a=h^2,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4490, #11797177, D3×#4505, … |
| maximal normal subgroup of | D3×#4490, #11797177, D3×#4505, … |
| maximal quotient of | #11772238, #11772373, #11773077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1023);