Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ #519 |
570 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 192 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=f,b^2=f,d^2=e,b^a=bf,h^a=h^2,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #11788551, #11857572, #11860655, … |
| maximal normal subgroup of | #11788551, #11857572, #11860655, … |
| maximal quotient of | #11800890, #11800891, #11800942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6127);