Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#63784 |
| Fitting | C2×C32×Q8 ⋊ C4 |
| Sylow | C32 ⋊ C2×#103 |
318 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63784, #103×#157, #11784040, … |
| maximal normal subgroup of | C4×#63784, #103×#157, #11784040, … |
| maximal quotient of | C2×Q8⋊#622, C2×#10590161, #11774206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5710);