Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #389 |
197 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 61 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=de,c^2=f,b^a=bd,c^a=cf,g^a=g^2h^2,h^a=g^2h,g^b=gh^2,h^b=g^2h^2,g^d=g^2,h^d=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #11786858, #11786906, #11786954, … |
| maximal normal subgroup of | #11786858, #11786906, #11786954, … |
| maximal quotient of | C4⋊#63747, #11773252, #11773377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5436);