Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C32 ⋊ #488 |
162 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 31 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|b^2=e,c^2=ef,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^2,c^b=ce,d^b=df,g^b=h,h^b=g,g^d=g^2,h^d=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593353, #11873461, #11873514, … |
| maximal normal subgroup of | C2×#10593353, #11873461, #11873514, … |
| maximal quotient of | #11786059, #11789781, #11789782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5235);