Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D4×#157 |
| Fitting | C2×C32×D4 ⋊ C4 |
| Sylow | C32 ⋊ C2×C4×D4 |
662 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11773799, #11773820, C2×D4⋊AGL(1,𝔽9), … |
| maximal normal subgroup of | #11773799, #11773820, C2×D4⋊AGL(1,𝔽9), … |
| maximal quotient of | C2×C22⋊C4×#157, C2×C4⋊C4×#157, C4×D4×#157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8523);