Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #330 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^2,h^a=h^2,d^b=df99 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#330, C2×#10589331, D3×#4465, … |
| maximal normal subgroup of | C3⋊D3×#330, C2×#10589331, D3×#4465, … |
| maximal quotient of | #11770665, #11770671, #11771066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1213);