Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #500 |
214 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 80 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:
2^6,3^2|a^2=d,b^2=d,c^2=ef,e^2=f,b^a=bd,h^a=h^2,c^b=ce,e^b=ef,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11799503, #11799506, #11799507, … |
| maximal normal subgroup of | #11799503, #11799506, #11799507, … |
| maximal quotient of | #11786233, #11790141, #11790143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2773);