Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#5152 |
| Sylow | C32 ⋊ #442 |
302 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 114 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 | C3×#71515, C3×#69254, #11797978, … |
| maximal normal subgroup of | C3×#71515, C3×#69254, #11797978, … |
| maximal quotient of | C3×#70878, C3×#70880, C3×#70882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4131);