Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×D3×H(5,𝔽2) |
| Fitting | C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ C2×H(5,𝔽2) |
1879 conjugacy classes of subgroups; only the 890 normal subgroups are shown.
This group has 1879 conjugacy classes of subgroups — too many to draw. Only its 890 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#453, D3×#5241, C3×D3×#455, … |
| maximal normal subgroup of | C3×D3×#453, D3×#5241, C3×D3×#455, … |
| maximal quotient of | C3×D3×#518, C3×D3×#520, C3×#85857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8619);