Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #398 |
177 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=de,c^2=ef,b^a=bd,c^a=ce,g^a=g^2h^2,h^a=g^2h,c^b=cf,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×#10593552, #11808734, #11808866, … |
| maximal normal subgroup of | C2×#10593552, #11808734, #11808866, … |
| maximal quotient of | #11773377, #11773378, #11773411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5434);