Finite Group DatabasebetaFinite Group Databasebeta| order | 24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C31 |
| unambiguous semidirect product | C13⋊(C31⋊D31) |
| unambiguous semidirect product | C31⋊D403 |
| Fitting, socle, derived, Hall | C13×C312 ⋊ C2 |
| Sylow | C312 ⋊ D13 |
| Sylow | C13 ⋊ C31⋊D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C312 | C2 |
| LCS | G ▷ C13×C312 | |
| UCS | C1 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12493 |
Polycyclic presentation:
2,13,31^2|b^a=b^12,c^a=c^30,d^a=d^306248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24986, 10);