Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#63805 |
| Sylow | C32 ⋊ C2×#131 |
570 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 192 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 | #11784105, #11784154, #11785566, … |
| maximal normal subgroup of | #11784105, #11784154, #11785566, … |
| maximal quotient of | C2×#10590909, C2×#10590703, C4×#63805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6578);