Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #407 |
342 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^6,3^2|b^2=e,e^2=f,b^a=bd,g^a=g^2,c^b=cf,g^b=h,h^b=g,g^d=g^2,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #11784648, #11784667, #11784692, … |
| maximal normal subgroup of | #11784648, #11784667, #11784692, … |
| maximal quotient of | #11773862, #11773863, #11773882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5189);