Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #529 |
522 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 138 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|d^2=ef,b^a=be,c^a=cf,h^a=h^2,c^b=cf,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11774445, #11774480, #11774817, … |
| maximal normal subgroup of | #11774445, #11774480, #11774817, … |
| maximal quotient of | #11801160, #11801519, #11801691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6915);