Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#106 |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=ef,c^2=f,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^2,c^b=cf,d^b=df,g^b=h,h^b=g,g^d=g^2,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11772483, #11785599, #11785600, … |
| maximal normal subgroup of | #11772483, #11785599, #11785600, … |
| maximal quotient of | #11776768, #11776880, #11776994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5269);