Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #357 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|b^2=d,c^2=ef,d^2=e,e^2=f,b^a=bc,c^a=ce,d^a=def,e^a=ef,g^a=g^2,g^b=h,h^b=g,g^c=g^2,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590016, #11796664, #11796697, … |
| maximal normal subgroup of | C2×#10590016, #11796664, #11796697, … |
| maximal quotient of | #11771579, #11771862, #11772071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1898);