Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×Dic18 |
| Sylow | C9 ⋊ C8×Q8 |
153 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 153 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) = 576 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11771673, #11771679, C8×#3672, … |
| maximal normal subgroup of | #11771673, #11771679, C8×#3672, … |
| maximal quotient of | C8×C4⋊Dic9, C8×Dic9⋊C4, #11788938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 240);