Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C2×C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #554 |
684 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 203 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|b^2=f,c^2=e,d^a=def,g^a=g^2,h^a=h^2,c^b=cf105 conjugacy classes — view the full character table.
| maximal subgroup of | #11887084, #11887090, #11887114, … |
| maximal normal subgroup of | #11887084, #11887090, #11887114, … |
| maximal quotient of | #11805210, #11805222, C4⋊C4×#638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7864);