Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#63509 |
| Fitting | C22×Q8×C9 ⋊ C2 |
| Sylow | C9 ⋊ C2×#124 |
495 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11787792, #11787891, #11787897, … |
| maximal normal subgroup of | #11787792, #11787891, #11787897, … |
| maximal quotient of | C2×#10588657, C2×#10588670, C2×#10588668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1798);