Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#984 |
295 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 295 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | #11920692, #11920700, #11920713, … |
| maximal normal subgroup of | #11920692, #11920700, #11920713, … |
| maximal quotient of | C2×C3×#5386, C2×C3×#5388, C3×#85319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8444);