Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C4×Q16 |
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=ef,c^2=ef,d^2=f,g^a=g^2,h^a=h^2,c^b=cd,d^b=df,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #11771591, #11771627, #11777231, … |
| maximal normal subgroup of | #11771591, #11771627, #11777231, … |
| maximal quotient of | #11777221, #11777516, #11777838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4454);