Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #324 |
181 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 181 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=c,c^2=e,b^a=bd,c^a=cf,h^a=h^2,d^b=df,g^b=g^278 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4469, #11773738, D3×#4528, … |
| maximal normal subgroup of | D3×#4469, #11773738, D3×#4528, … |
| maximal quotient of | #11770675, #11770677, #11770811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1029);