Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #396 |
253 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=d,b^a=bdf,c^a=cf,g^a=g^2h^2,h^a=g^2h,c^b=ce,g^b=gh^2,h^b=g^2h^2,g^d=g^2,h^d=h^230 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593567, #11808734, #11810273, … |
| maximal normal subgroup of | C2×#10593567, #11808734, #11810273, … |
| maximal quotient of | #11773324, #11773378, #11773431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5449);