Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#5429 |
| Fitting | C3×H(5,𝔽2) ⋊ D3 |
167 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5429, #11922454, #11922455, … |
| maximal normal subgroup of | D3×#5429, #11922454, #11922455, … |
| maximal quotient of | C3×#73076, C3×#73078, C3×#73090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5497);