Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #405 |
390 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 207 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=d,c^2=e,d^2=f,e^2=f,g^a=g^2,h^a=h^2,c^b=cf120 conjugacy classes — view the full character table.
| maximal subgroup of | #11772332, #11772354, #11783526, … |
| maximal normal subgroup of | #11772332, #11772354, #11783526, … |
| maximal quotient of | M16×C3⋊(C3⋊C8), #11773564, #11773587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4703);