Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #358 |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=f,d^2=ef,e^2=f,g^3=h^2,b^a=bd,d^a=de,e^a=ef,g^a=g^2h,h^a=h^2,d^b=de,e^b=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#358, C2×#10588241, #11796639, … |
| maximal normal subgroup of | D9×#358, C2×#10588241, #11796639, … |
| maximal quotient of | #11771584, #11771867, #11772077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 123);