Finite Group DatabasebetaFinite Group Databasebeta| order | 16185 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C83 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C5×C13×C83 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C5×C83 |
| Hall | C13×C83 ⋊ C3×C5 |
| Hall | C5×C13 ⋊ C3×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C83 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C5×C83 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C83 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C5×C83 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5395 |
2905 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C13⋊C3×C83, C5×C13⋊C3×D83, C5×D13⋊C3×C83, … |
| maximal normal subgroup of | C2×C5×C13⋊C3×C83, C5×C13⋊C3×D83, C5×D13⋊C3×C83, … |
| maximal quotient of | C2×C5×C13⋊C3×C83 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16185, 2);