Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
124 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^2,2^2|b^2=c,c^2=d,e^3=f^2,b^a=bd,e^a=e^2f,f^a=f^2,g^a=h,h^a=g,g^e=h,h^e=gh60 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10589502, #11920336, M16×(C22⋊C9)⋊C2, … |
| maximal normal subgroup of | C2×#10589502, #11920336, M16×(C22⋊C9)⋊C2, … |
| maximal quotient of | #11919964, #11919965, #11919973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1384);