Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #444 |
239 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=d,d^2=f,b^a=bf,c^a=cde,h^a=h^2,g^b=g^2,e^c=ef66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4823, #11861053, D3×#5145, … |
| maximal normal subgroup of | D3×#4823, #11861053, D3×#5145, … |
| maximal quotient of | #11777278, #11777285, #11777320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3545);