Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #440 |
287 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 72 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=e,b^2=f,c^2=e,d^2=f,c^a=cd,d^a=df,h^a=h^2,c^b=cdf,d^b=df,g^b=g^2,d^c=df60 conjugacy classes — view the full character table.
| maximal subgroup of | #11860061, C2×#10590484, D3×#4889, … |
| maximal normal subgroup of | #11860061, C2×#10590484, D3×#4889, … |
| maximal quotient of | #11777289, #11777598, #11777727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2366);