Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #499 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=e,c^2=d,e^2=f,c^a=cdf,g^a=g^2,h^a=h^2,c^b=cef,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11799734, #11799737, #11799745, … |
| maximal normal subgroup of | #11799734, #11799737, #11799745, … |
| maximal quotient of | #11786242, #11790090, #11790099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4439);