Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | Dic3×#239 |
| Sylow | C32 ⋊ C4×#41 |
655 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 655 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#916, #11860021, #11860023, … |
| maximal normal subgroup of | Dic3×#916, #11860021, #11860023, … |
| maximal quotient of | Dic3×#892, Dic3×#893, Q8×Dic32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7263);