Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ #529 |
702 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 197 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=df,g^a=g^2,h^a=h^2,d^b=def108 conjugacy classes — view the full character table.
| maximal subgroup of | #11774413, #11774435, #11774449, … |
| maximal normal subgroup of | #11774413, #11774435, #11774449, … |
| maximal quotient of | #11801135, #11801487, #11801660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7910);