Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | Dic3×#208 |
| Sylow | C32 ⋊ C4×M16 |
318 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11783784, Dic3×#823, #11783788, … |
| maximal normal subgroup of | #11783784, Dic3×#823, #11783788, … |
| maximal quotient of | #11773548, C3⋊C8×#208, #11773609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2936);