Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D32×C22⋊C4 |
| Fitting | C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C22×C22⋊C4 |
1414 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1414 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #11788254, C22⋊C4×GO+(4,𝔽2), #11805039, … |
| maximal normal subgroup of | #11788254, C22⋊C4×GO+(4,𝔽2), #11805039, … |
| maximal quotient of | D32×#95, D3×#4666, #11800698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6134);