Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C9 ⋊ C2 |
| Sylow | C9 ⋊ #431 |
177 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 81 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=d,d^2=f,g^3=h^2,c^a=ce,g^a=g^2h,h^a=h^2168 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#3663, #11773528, #11773557, … |
| maximal normal subgroup of | C8×#3663, #11773528, #11773557, … |
| maximal quotient of | #11783468, C4×(C2×D9)⋊C8, C4×Dic9⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 249);