Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#64153 |
| Sylow | C32 ⋊ C2×C4⋊Q8 |
870 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 870 conjugacy classes of subgroups — too many to draw. Only its 295 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590220, #11776355, #11776659, … |
| maximal normal subgroup of | C2×#10590220, #11776355, #11776659, … |
| maximal quotient of | C2×#10592674, C2×#10592675, C2×#10592672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8163);