Finite Group DatabasebetaFinite Group Databasebeta| order | 10225 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C3×C4×C5×C8×C17 (order 8160) · Inn(G) = C1 · Out(G) = C3×C4×C5×C8×C17 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10225 |
| abelian | C25×C409 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5 | C5×C409 |
| socle, prime radical | C5×C409 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6 conjugacy classes of subgroups.
10225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10225, 1);