Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #408 |
350 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 78 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|c^2=d,d^2=f,b^a=bf,c^a=ce,h^a=h^2,c^b=cef,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11771433, #11787658, #11792669, … |
| maximal normal subgroup of | #11771433, #11787658, #11792669, … |
| maximal quotient of | #11774006, #11774037, #11774065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2841);