Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
149 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 149 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) = 96 |
Polycyclic presentation:
2^3,3^2,2^3|b^2=c,c^2=h,f^2=h,g^2=h,b^a=bc,c^a=ch,e^a=e^2,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 | #11921837, #11921840, #11921846, … |
| maximal normal subgroup of | #11921837, #11921840, #11921846, … |
| maximal quotient of | #11920508, #11920516, #11920546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5114);