Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #423 |
306 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 90 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:
2^6,3^2|a^2=d,b^2=d,c^2=e,d^2=f,b^a=bf,c^a=ce,h^a=h^2,c^b=ce,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11770926, #11771025, #11771131, … |
| maximal normal subgroup of | #11770926, #11771025, #11771131, … |
| maximal quotient of | #11776876, #11776899, #11776926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2222);