Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ #413 |
450 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 450 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) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=f,c^2=d,d^2=f,c^a=ce,d^a=df,g^a=g^2,h^a=h^2,e^c=ef102 conjugacy classes — view the full character table.
| maximal subgroup of | #11783822, #11783828, #11783850, … |
| maximal normal subgroup of | #11783822, #11783828, #11783850, … |
| maximal quotient of | #11773750, #11773778, #11773888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4713);