Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×#611 |
| Fitting | C22×D4×C9 ⋊ C2 |
| Sylow | C9 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D9 |
| commutator, cosocle | C22×C9 | C24 |
| Frattini, socle | C22×C3 | C23×D3 |
| Fitting | C22×D4×C9 | C2 |
| hypercenter | C22×D4 | D9 |
| hypocenter | C9 | D42 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
642 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #11883738, #11883750, #11883756, … |
| maximal normal subgroup of | #11883738, #11883750, #11883756, … |
| maximal quotient of | D4×(C2×D9)⋊C4, C22⋊C4×#611, D4×#3676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1785);