Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^3,3^2,2^3|b^2=c,c^2=h,d^3=e^2,f^2=h,g^2=h,b^a=bc,c^a=ch,d^a=d^2e,e^a=e^2,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10589508, #11920350, #11920353, … |
| maximal normal subgroup of | C2×#10589508, #11920350, #11920353, … |
| maximal quotient of | #11919966, #11919971, #11919976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1390);