Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D9 |
| Fitting | C4×Q8×C9 ⋊ C2 |
| Sylow | C9 ⋊ C2×C4×Q8 |
447 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 201 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 | D9×Q8⋊C8, #11774325, #11774569, … |
| maximal normal subgroup of | D9×Q8⋊C8, #11774325, #11774569, … |
| maximal quotient of | C4×C4⋊C4×D9, C4×#63449, C4×Q8×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1555);