Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#3675 |
| Fitting | C4×Q8×C9 ⋊ C2 |
| Sylow | C9 ⋊ C4×SD16 |
183 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11777164, C8×#3675, #11777251, … |
| maximal normal subgroup of | #11777164, C8×#3675, #11777251, … |
| maximal quotient of | C8×#3675, #11777414, #11777469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 590);