Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#63791 |
| Fitting | C2×C32×C8 ⋊ C22 |
| Sylow | C32 ⋊ C22×M16 |
634 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11783739, #11783740, #11785418, … |
| maximal normal subgroup of | #11783739, #11783740, #11785418, … |
| maximal quotient of | C2×#10590668, C4×#63791, C2×#10590667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6548);