Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #473 |
160 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 29 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=f,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^2,c^b=ce,d^b=df,e^b=ef,g^b=h,h^b=g,e^c=ef,g^d=g^2,h^d=h^230 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593468, #11867997, #11868067, … |
| maximal normal subgroup of | C2×#10593468, #11867997, #11868067, … |
| maximal quotient of | #11780968, #11781001, #11781128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5350);