Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #510 |
246 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf,d^c=de,e^c=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | #11797898, #11797907, #11797925, … |
| maximal normal subgroup of | #11797898, #11797907, #11797925, … |
| maximal quotient of | #11796676, #11796729, #11797223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4776);