Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
129 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 129 conjugacy classes of subgroups — too many to draw. Only its 21 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:
2^3,3^2,2^3|a^2=c,b^2=h,c^2=h,f^2=h,g^2=h,b^a=bc,e^a=e^2,c^b=ch,d^b=d^2,f^b=gh,g^b=fh,f^d=g,g^d=fgh,g^f=gh33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5403, #11921820, #11921821, … |
| maximal normal subgroup of | D3×#5403, #11921820, #11921821, … |
| maximal quotient of | #11920526, #11920528, #11920531, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5108);