Finite Group DatabasebetaFinite Group Databasebeta| order | 49729 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 49506 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C49729 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, socle, prime radical, cosocle | C223 | C223 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C223 ▷ C1 | |
3 conjugacy classes of subgroups.
49729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(49729, 1);