Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C9 ⋊ M64 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=c,c^2=d,d^2=e,e^2=f,g^3=h^2,b^a=bf,g^a=g^2h,h^a=h^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #11772671, #11772674, #11772698, … |
| maximal normal subgroup of | #11772671, #11772674, #11772698, … |
| maximal quotient of | #11772660, #11772688, C4⋊(C9⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 58);