Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×Dic24 |
| Sylow | C32 ⋊ C2×Q32 |
178 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67578, C3×#67597, #11772933, … |
| maximal normal subgroup of | C3×#67578, C3×#67597, #11772933, … |
| maximal quotient of | C2×C3×#4503, C2×C3×#4504, C3×C4×Dic24, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3884);