Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#939 |
| Fitting | C2×C32×D4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Fitting | C2×C32×D4 | C22 |
| hypercenter | C2×D4 | D32 |
| hypocenter | C32 | C2×#121 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
899 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#121, C2×D3×#939, D3×#5586, … |
| maximal normal subgroup of | D32×#121, C2×D3×#939, D3×#5586, … |
| maximal quotient of | D3×#4942, D3×#4958, D3×#5220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7165);