Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #343 |
294 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,d^2=f,b^a=be,d^a=df,g^a=g^2,h^a=h^2,e^b=ef102 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#343, C2×#10589420, D3×#4554, … |
| maximal normal subgroup of | C3⋊D3×#343, C2×#10589420, D3×#4554, … |
| maximal quotient of | #11770804, #11770852, #11770858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1302);