Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C9×M32 ⋊ C2 |
| Sylow | C9 ⋊ #349 |
87 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=c,c^2=e,e^2=f,g^3=h^2,b^a=bd,c^a=cf,g^a=g^2h,h^a=h^2,d^b=df102 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#349, C2×#10588191, #11796044, … |
| maximal normal subgroup of | D9×#349, C2×#10588191, #11796044, … |
| maximal quotient of | #11771334, #11771434, #11771544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 73);