Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×C4⋊Q8 ⋊ C2 |
| Sylow | C32 ⋊ D4×Q8 |
840 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 211 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=e,c^2=e,d^2=f,d^a=def,g^a=g^2,h^a=h^2,c^b=ce,d^c=df81 conjugacy classes — view the full character table.
| maximal subgroup of | #11779196, #11779208, #11779220, … |
| maximal normal subgroup of | #11779196, #11779208, #11779220, … |
| maximal quotient of | #11804872, #11805418, #11805421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8080);