Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×C22⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ #407 |
570 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|c^2=d,d^2=f,c^a=cf,g^a=g^2,h^a=h^2,c^b=ce108 conjugacy classes — view the full character table.
| maximal subgroup of | #11770882, #11771034, #11771233, … |
| maximal normal subgroup of | #11770882, #11771034, #11771233, … |
| maximal quotient of | #11773845, #11773865, #11773885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4307);