Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | Q8×C3⋊S4 |
| Fitting | C22×C3×Q8 ⋊ D3 |
388 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | #11922199, #11922204, #11922207, … |
| maximal normal subgroup of | #11922199, #11922204, #11922207, … |
| maximal quotient of | #11922851, #11922852, #11922853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8463);