Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C24×C32 ⋊ C4 |
| Sylow | C32 ⋊ AΣL(1,𝔽16) |
224 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 18 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^a=bd,d^a=de,e^a=ef,g^a=gh,h^a=gh^2,c^b=ce,d^c=df,g^c=g^2,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590223, #11796143, #11796200, … |
| maximal normal subgroup of | C2×#10590223, #11796143, #11796200, … |
| maximal quotient of | #11771366, #11771493, #11771788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2105);