Finite Group DatabasebetaFinite Group Databasebeta| order | 13845 |
| isoclinism | isoclinic class of C71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×C71⋊C5 |
| unambiguous semidirect product | C71⋊(C3×C5×C13) |
| unambiguous semidirect product | (C3×C71)⋊(C5×C13) |
| unambiguous semidirect product | (C3×C13×C71)⋊C5 |
| Fitting, socle, Hall | C3×C13×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C3×C5×C13 |
| Hall | C13×C71 ⋊ C3×C5 |
| Hall | C3×C71 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C71⋊C5 |
| commutator, cosocle, hypocenter | C71 | C3×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C3×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2769 |
741 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C13×C71⋊C5, C3×C13×D71⋊C5, C3×D13×C71⋊C5, … |
| maximal normal subgroup of | C2×C3×C13×C71⋊C5, C3×C13×D71⋊C5, C3×D13×C71⋊C5, … |
| maximal quotient of | C2×C3×C13×C71⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13845, 2);