Finite Group DatabasebetaFinite Group Databasebeta| order | 16165 |
| isoclinism | isoclinic class of C61⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C61⋊C5 |
| unambiguous semidirect product | C61⋊(C5×C53) |
| unambiguous semidirect product | (C53×C61)⋊C5 |
| Fitting, socle, Hall | C53×C61 ⋊ C5 |
| derived, Sylow | C61 ⋊ C5×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C53×C61 | C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C53 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3233 |
901 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C53×C61⋊C5, C53×D61⋊C5, D53×C61⋊C5, … |
| maximal normal subgroup of | C2×C53×C61⋊C5, C53×D61⋊C5, D53×C61⋊C5, … |
| maximal quotient of | C2×C53×C61⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16165, 1);