Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C9 ⋊ #340 |
171 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=de,d^2=f,g^3=h^2,b^a=bd,d^a=df,g^a=g^2h,h^a=h^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #11771850, #11771853, #11771867, … |
| maximal normal subgroup of | #11771850, #11771853, #11771867, … |
| maximal quotient of | #11770749, #11770784, #11770912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 111);