Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #468 |
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^2,c^b=cef,d^c=df72 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#468, C2×#10592741, D3×#5042, … |
| maximal normal subgroup of | C3⋊D3×#468, C2×#10592741, D3×#5042, … |
| maximal quotient of | #11781604, #11781650, #11781827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4623);