Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
286 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 286 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) = 72 |
Polycyclic presentation:
2^4,3^2,2^2|b^2=d,c^2=d,e^3=f,c^a=cd,e^a=e^2f^2,f^a=f^2,g^a=h,h^a=g,c^b=cd,g^e=h,h^e=gh45 conjugacy classes — view the full character table.
| maximal subgroup of | #11920359, #11920361, #11920363, … |
| maximal normal subgroup of | #11920359, #11920361, #11920363, … |
| maximal quotient of | #11920205, #11920207, #11920208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4976);