Finite Group DatabasebetaFinite Group Databasebeta| order | 10375 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C25×C41 (order 8200) · Inn(G) = C1 · Out(G) = C2×C4×C25×C41 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10375 |
| abelian | C83×C125 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C25 | C5×C83 |
| socle, prime radical | C5×C83 | C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
10375 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic10375, C2×D10375 |
| maximal subgroup of | C2×C83×C125, C3×C83×C125, D10375 |
| maximal normal subgroup of | C2×C83×C125, C3×C83×C125, D10375 |
| maximal quotient of | C2×C83×C125, C3×C83×C125 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10375, 1);