Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C32×C8 ⋊ D4 |
| Sylow | C32 ⋊ #436 |
190 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^2,c^b=cf,g^b=h,h^b=g,g^d=g^2,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11771562, #11777508, #11777830, … |
| maximal normal subgroup of | #11771562, #11777508, #11777830, … |
| maximal quotient of | #11777780, #11777781, #11777828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5165);