Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×C8 ⋊ Q8 |
| Sylow | C32 ⋊ #446 |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,g^a=g^2h^2,h^a=g^2h,c^b=cf,g^b=gh^2,h^b=g^2h^2,g^d=g^2,h^d=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #11771710, #11777459, #11777830, … |
| maximal normal subgroup of | #11771710, #11777459, #11777830, … |
| maximal quotient of | #11784309, #11784357, #11788980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5414);