Finite Group DatabasebetaFinite Group Databasebeta| order | 10547 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C9×C11×C13 (order 10296) · Inn(G) = C1 · Out(G) = C2×C4×C9×C11×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10547 |
| abelian | C53×C199 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4 conjugacy classes of subgroups.
10547 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C53×C199⋊C3 |
| socle of | C53×C199⋊C3 |
| maximal subgroup of | D53×C199, C53×D199, D10547, … |
| maximal normal subgroup of | D53×C199, C53×D199, D10547, … |
| maximal quotient of | C2×C53×C199, C3×C53×C199 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10547, 1);