Finite Group DatabasebetaFinite Group Databasebeta| order | 13858 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×D41 |
| unambiguous semidirect product | C41⋊(C2×C132) |
| Fitting, socle, Hall | C132×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D41 |
| commutator, cosocle, hypocenter | C41 | C2×C132 |
| Frattini | C1 | G |
| Fitting, socle | C132×C41 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C132 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6929 |
3718 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C132×#4223, C13×#14523824, C13×D13×D41, … |
| maximal normal subgroup of | C132×#4223, C13×#14523824, C13×D13×D41, … |
| maximal quotient of | C132×Dic41, C2×C132×D41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13858, 10);