Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C491 · Schur multiplier (H2) = C22 |
| direct product | C4⋊Q8×C491 |
| unambiguous semidirect product | C4⋊(Q8×C491) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C491 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C491 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C491 ◁ G | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
6874 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 35);