Finite Group DatabasebetaFinite Group Databasebeta| order | 16023 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×C49⋊C3 |
| unambiguous semidirect product | C49⋊(C3×C109) |
| Fitting, Hall | C49×C109 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C3×C109 |
| Frattini | C7 | ΓL(1,𝔽8)×C109 |
| Fitting | C49×C109 | C3 |
| socle | C7×C109 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C109 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5341 |
2071 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C109×C49⋊C3, C49⋊C3×D109, C109×D49⋊C3, … |
| maximal normal subgroup of | C2×C109×C49⋊C3, C49⋊C3×D109, C109×D49⋊C3, … |
| maximal quotient of | C2×C109×C49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16023, 2);