Finite Group DatabasebetaFinite Group Databasebeta| order | 10049 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C3×C42×C193 (order 9264) · Inn(G) = C1 · Out(G) = C3×C42×C193 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10049 |
| abelian | C13×C773 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4 conjugacy classes of subgroups.
10049 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C13⋊C3×C773 |
| socle of | C13⋊C3×C773 |
| maximal subgroup of | D13×C773, C13×D773, D10049, … |
| maximal normal subgroup of | D13×C773, C13×D773, D10049, … |
| maximal quotient of | C2×C13×C773, C3×C13×C773 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10049, 1);