Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#63741 |
| Sylow | C32 ⋊ C2×#104 |
306 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63741, #11783923, #11784806, … |
| maximal normal subgroup of | C4×#63741, #11783923, #11784806, … |
| maximal quotient of | C2×#10590030, C2×#10590031, #11774258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5387);