Finite Group DatabasebetaFinite Group Databasebeta| order | 16005 |
| isoclinism | isoclinic class of C97⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×C97⋊C3 |
| unambiguous semidirect product | C97⋊(C3×C5×C11) |
| unambiguous semidirect product | (C5×C97)⋊(C3×C11) |
| unambiguous semidirect product | (C5×C11×C97)⋊C3 |
| Fitting, socle, Hall | C5×C11×C97 ⋊ C3 |
| derived, Sylow | C97 ⋊ C3×C5×C11 |
| Hall | C11×C97 ⋊ C3×C5 |
| Hall | C5×C97 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | C97⋊C3 |
| commutator, cosocle, hypocenter | C97 | C3×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C97 | C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C5×C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5335 |
1925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C11×C97⋊C3, C5×C11×D97⋊C3, C5×D11×C97⋊C3, … |
| maximal normal subgroup of | C2×C5×C11×C97⋊C3, C5×C11×D97⋊C3, C5×D11×C97⋊C3, … |
| maximal quotient of | C2×C5×C11×C97⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16005, 3);