Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C9 ⋊ #365 |
63 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,d^2=e,e^2=f,g^3=h^2,b^a=bd,d^a=de,e^a=ef,g^a=g^2h,h^a=h^2,c^b=cf96 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#365, C2×#10588190, #11797116, … |
| maximal normal subgroup of | D9×#365, C2×#10588190, #11797116, … |
| maximal quotient of | #11772178, #11772417, C2×#10588190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 72);