Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4621 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#4622 |
| Fitting | C3×#95 ⋊ D3 |
| derived | #95⋊C3 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #857 |
| commutator, cosocle, hypocenter | #95⋊C3 | C2×C3 |
| Frattini | C23 | C3×S4 |
| Fitting | C3×#95 | D3 |
| socle | C23×C3 | S4 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | #11920469, #11920470, #11920473, … |
| maximal normal subgroup of | #11920469, #11920470, #11920473, … |
| maximal quotient of | C3×#67993, C3×#67994, C3×SL(2,ℤ/8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1982);