Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#99 |
486 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 486 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) = 24 |
Polycyclic presentation:
2^6,3^2|c^2=d,c^a=ce,d^a=df,h^a=h^2,c^b=ce,d^b=df,g^b=g^2,e^c=ef54 conjugacy classes — view the full character table.
| maximal subgroup of | #11788254, #11788288, #11788864, … |
| maximal normal subgroup of | #11788254, #11788288, #11788864, … |
| maximal quotient of | #11773717, #11773738, #11773791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2286);