Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D9)⋊C8 |
| Fitting | C22×C8×C9 ⋊ C2 |
| Sylow | C9 ⋊ C2×C22⋊C8 |
303 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11771334, #11783542, C4×(C2×D9)⋊C8, … |
| maximal normal subgroup of | #11771334, #11783542, C4×(C2×D9)⋊C8, … |
| maximal quotient of | C2×#10588146, C2×#10588145, #11773749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 671);