Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #427 |
141 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=de,c^2=f,d^2=f,e^2=f,b^a=bd,g^a=g^2h^2,h^a=g^2h,d^b=df,e^b=ef,g^b=gh^2,h^b=g^2h^2,g^d=g^2,h^d=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #11772413, #11772448, #11772483, … |
| maximal normal subgroup of | #11772413, #11772448, #11772483, … |
| maximal quotient of | #11776823, #11776824, #11776933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5425);