Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63511 |
| Sylow | C9 ⋊ C2×#137 |
387 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #11787662, #11787668, #11788363, … |
| maximal normal subgroup of | #11787662, #11787668, #11788363, … |
| maximal quotient of | C2×#10588681, C2×#10588916, C2×#10588679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1804);