Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#63783 |
| Fitting | C2×C32×D4 ⋊ C4 |
| Sylow | C32 ⋊ C2×#104 |
334 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63783, #11783905, #11784082, … |
| maximal normal subgroup of | C4×#63783, #11783905, #11784082, … |
| maximal quotient of | C2×D4⋊#622, C2×#10590161, #11774239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5697);