Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C4 |
| direct product | C4×C42⋊C9 |
| unambiguous semidirect product | C43⋊C9 |
| derived | C42 ⋊ C4×C9 |
| Sylow | C43 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C42⋊C3 |
| commutator, hypocenter | C42 | C4×C9 |
| Frattini, socle, prime radical | C23×C3 | C2×A4 |
| Fitting | C3×C43 | C3 |
| cosocle | C2×C3×C42 | C2×C3 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C3×C4 | |
107 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C8×C42⋊C9, #1839⋊C9, #1842⋊C9, … |
| maximal normal subgroup of | C8×C42⋊C9, #1839⋊C9, #1842⋊C9, … |
| maximal quotient of | C4×#95⋊C9, C8×C42⋊C9, #1726⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 191);