Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5731 |
| Fitting | C32×C4⋊Q8 ⋊ C2 |
| Sylow | C32 ⋊ #541 |
418 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#80412, C3×#80460, #11872495, … |
| maximal normal subgroup of | C3×#80412, C3×#80460, #11872495, … |
| maximal quotient of | C3×#74358, C3×#76483, C3×#76611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7710);