Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #354 |
105 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 105 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=c,d^2=f,g^3=h^2,b^a=bd,c^a=ce,d^a=df,g^a=g^2h,h^a=h^2,d^b=def,e^b=ef,d^c=df57 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#354, C2×#10588149, #11796353, … |
| maximal normal subgroup of | D9×#354, C2×#10588149, #11796353, … |
| maximal quotient of | #11771396, #11771459, #11771796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 31);