Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C4⋊C4×#157 |
| Fitting | C32×C4⋊C4 ⋊ C4 |
| Sylow | C32 ⋊ C4×C4⋊C4 |
286 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11770796, #102×#157, #103×#157, … |
| maximal normal subgroup of | #11770796, #102×#157, #103×#157, … |
| maximal quotient of | #95×#157, #11773183, #11773206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5639);