Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#41×D9 |
| Fitting | C2×C9×#41 ⋊ C2 |
| Sylow | C9 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D9 |
| commutator, cosocle | C2×C9 | C25 |
| Frattini | C2×C3 | C24×D3 |
| Fitting | C2×C9×#41 | C2 |
| socle | C22×C3 | C23×D3 |
| hypercenter | C2×#41 | D9 |
| hypocenter | C9 | C22×#41 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
1335 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1335 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11784782, D9×#408, #11857411, … |
| maximal normal subgroup of | #11784782, D9×#408, #11857411, … |
| maximal quotient of | C2×D9×#117, C2×C4×D4×D9, C2×C4×Q8×D9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5018);