Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ AΣL(1,𝔽16) |
253 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 253 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=cd,b^a=bd,d^a=de,e^a=ef,h^a=h^2,c^b=ce,d^b=de,e^b=ef,g^b=g^2,d^c=df45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4471, #11796147, C2×#10589174, … |
| maximal normal subgroup of | D3×#4471, #11796147, C2×#10589174, … |
| maximal quotient of | #11771369, #11771495, #11771791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1056);