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=d,b^2=cd,c^2=e,d^2=f,g^3=h^2,b^a=bc,c^a=ce,g^a=g^2h,h^a=h^2156 conjugacy classes — view the full character table.
| maximal subgroup of | D9×Q8⋊C8, C2×#10588133, #11774222, … |
| maximal normal subgroup of | D9×Q8⋊C8, C2×#10588133, #11774222, … |
| maximal quotient of | #11770670, #11770683, #11770784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 15);