Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×Q8×Dic6 |
| Sylow | C32 ⋊ Q82 |
459 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 459 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 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71033, C3×#68264, #11779057, … |
| maximal normal subgroup of | C3×#71033, C3×#68264, #11779057, … |
| maximal quotient of | C3×Q8×Dic3⋊C4, C3×C4⋊C4×Dic6, C3×Q8×C4⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7545);