Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#63383 |
| Fitting | C2×C9×M16 ⋊ C2 |
| Sylow | C9 ⋊ C2×#100 |
279 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #11783769, C4×#63383, #11784630, … |
| maximal normal subgroup of | #11783769, C4×#63383, #11784630, … |
| maximal quotient of | C2×#10588146, #11773805, #11773847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 694);