Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×D32⋊C8 |
| Sylow | C32 ⋊ C2×C22⋊C8 |
358 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D32⋊C8, #11783592, #11783624, … |
| maximal normal subgroup of | C4×D32⋊C8, #11783592, #11783624, … |
| maximal quotient of | C2×#10590027, #11773724, C2×#10590028, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5188);