Finite Group DatabasebetaFinite Group Databasebeta| order | 10001 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C82×C9×C17 (order 9792) · Inn(G) = C1 · Out(G) = C82×C9×C17 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10001 |
| abelian | C73×C137 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4 conjugacy classes of subgroups.
10001 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C137×C73⋊C3 |
| socle of | C137×C73⋊C3 |
| maximal subgroup of | C137×D73, C73×D137, D10001, … |
| maximal normal subgroup of | C137×D73, C73×D137, D10001, … |
| maximal quotient of | C2×C73×C137, C3×C73×C137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10001, 1);