Finite Group DatabasebetaFinite Group Databasebeta| order | 13924 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C59 |
| unambiguous semidirect product | C59⋊Dic59 |
| derived, Sylow | C592 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C59⋊D59 |
| commutator, hypocenter | C592 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C592 | C2 |
| LCS | G ▷ C592 | |
| UCS | C1 ◁ C2 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13924 |
Polycyclic presentation:
2,59^2,2|a^2=d,b^a=b^58,c^a=c^583484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13924, 7);