Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C9 ⋊ #368 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=de,c^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^2150 conjugacy classes — view the full character table.
| maximal subgroup of | #11772942, #11772945, #11772976, … |
| maximal normal subgroup of | #11772942, #11772945, #11772976, … |
| maximal quotient of | #11772220, #11772233, #11772382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 65);