Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ Q8⋊C8 |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=c,c^2=e,d^2=f,g^3=h^2,b^a=bd,d^a=df,g^a=g^2h,h^a=h^2,d^b=df108 conjugacy classes — view the full character table.
| maximal subgroup of | D9×Q8⋊C8, C2×#10588160, #11774222, … |
| maximal normal subgroup of | D9×Q8⋊C8, C2×#10588160, #11774222, … |
| maximal quotient of | #11770664, #11770683, #11770781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 42);