Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#3688 |
113 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^3,3^2,2^3|a^2=h,b^2=c,d^3=e^2,f^2=h,g^2=h,b^a=bc,d^a=d^2e,e^a=e^2,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh51 conjugacy classes — view the full character table.
| maximal subgroup of | #11919966, #11919967, #11919970, … |
| maximal normal subgroup of | #11919966, #11919967, #11919970, … |
| maximal quotient of | #11919966, #11919967, #11919968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1374);