Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ #518 |
507 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|d^2=e,g^3=h,c^a=cf,g^a=g^2h^2,h^a=h^2,d^b=df114 conjugacy classes — view the full character table.
| maximal subgroup of | #11785898, #11787056, #11787065, … |
| maximal normal subgroup of | #11785898, #11787056, #11787065, … |
| maximal quotient of | #11800852, #11800855, #11800869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1470);