Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C4×#3755 |
| Fitting | C32×C4×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C4×SD16 |
366 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 127 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 | #11777165, C8×#3755, #11777194, … |
| maximal normal subgroup of | #11777165, C8×#3755, #11777194, … |
| maximal quotient of | C8×#3755, #11777415, #11777470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4606);