Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | M16×C3⋊Dic3 |
| Sylow | C32 ⋊ C4×M16 |
426 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11770772, #11770862, M16×#622, … |
| maximal normal subgroup of | #11770772, #11770862, M16×#622, … |
| maximal quotient of | M16×C3⋊(C3⋊C8), #11773535, #11773587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4698);