Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#63647 |
| Fitting | C22×C32×C8 ⋊ C2 |
| Sylow | C32 ⋊ C2×C22⋊C8 |
606 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 207 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 | #11770841, #11770975, #11771035, … |
| maximal normal subgroup of | #11770841, #11770975, #11771035, … |
| maximal quotient of | C2×#10589334, C2×#10589335, #11773750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4689);