Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #499 |
129 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,g^3=h^2,c^a=cdf,g^a=g^2h,h^a=h^2,c^b=ce,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11799609, #11799612, #11799621, … |
| maximal normal subgroup of | #11799609, #11799612, #11799621, … |
| maximal quotient of | #11786247, #11790092, #11790123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 440);