Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×(C2×S4)⋊C4 |
| unambiguous semidirect product | (C2×S4)⋊(C3×C4) |
| Fitting | C23×C3×C4 ⋊ D3 |
302 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #11921892, #11921894, #11921912, … |
| maximal normal subgroup of | #11921892, #11921894, #11921912, … |
| maximal quotient of | C3×#73046, C3×#73049, C3×#73052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5481);