Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #423 |
234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=f,c^2=ef,d^2=f,b^a=bf,c^a=ce,g^a=gh,h^a=gh^2,g^d=g^2,h^d=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11770919, #11771020, #11771126, … |
| maximal normal subgroup of | #11770919, #11771020, #11771126, … |
| maximal quotient of | #11776872, #11776895, #11776921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5611);