Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #427 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^2,c^b=cf,d^b=df,g^b=h,h^b=g,g^d=g^2,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11772412, #11772546, #11785501, … |
| maximal normal subgroup of | #11772412, #11772546, #11785501, … |
| maximal quotient of | #11776822, #11776932, #11777057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5393);