Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #462 |
168 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 33 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,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^2,c^b=ce,e^b=ef,g^b=h,h^b=g,e^c=ef,g^d=g^2,h^d=h^233 conjugacy classes — view the full character table.
| maximal subgroup of | #11780032, #11780411, #11781097, … |
| maximal normal subgroup of | #11780032, #11780411, #11781097, … |
| maximal quotient of | #11781095, #11781096, #11781161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5359);