Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #475 |
165 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=ef,c^2=ef,d^2=f,b^a=bd,c^a=cef,d^a=df,g^a=g^2,c^b=cf,d^b=df,g^b=h,h^b=g,g^d=g^2,h^d=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | #11779790, #11779884, #11779932, … |
| maximal normal subgroup of | #11779790, #11779884, #11779932, … |
| maximal quotient of | #11785225, #11787002, #11789119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5267);