Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C2×C32×C8 ⋊ C4 |
| Sylow | C32 ⋊ #344 |
158 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 34 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|a^2=c,b^2=d,d^2=f,b^a=be,e^a=ef,g^a=gh,h^a=gh^2,c^b=cf,g^c=g^2,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590183, #11783445, #11783836, … |
| maximal normal subgroup of | C2×#10590183, #11783445, #11783836, … |
| maximal quotient of | #11770824, #11770841, #11770861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2065);