Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5570 |
| Sylow | C32 ⋊ #557 |
435 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 435 conjugacy classes of subgroups — too many to draw. Only its 230 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×#71030, C3×#68252, #11779183, … |
| maximal normal subgroup of | C3×#71030, C3×#68252, #11779183, … |
| maximal quotient of | C3×Q8×C4⋊Dic3, C3×#82461, C3×#73640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7549);