Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C491 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊C4×C491 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C491 | C22 |
| commutator | C2 | C22×C4×C491 |
| Frattini, cosocle | C22 | C23×C491 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C491 ◁ G | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
9820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 23);