Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #41×Dic9 |
| Sylow | C9 ⋊ C4×#41 |
465 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 265 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #104×Dic9, #11783899, #11785301, … |
| maximal normal subgroup of | #104×Dic9, #11783899, #11785301, … |
| maximal quotient of | #117×Dic9, C4×D4×Dic9, C4×Q8×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1810);