Finite Group DatabasebetaFinite Group Databasebeta| order | 8875 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C5×C7×C25 (order 7000) · Inn(G) = C1 · Out(G) = C2×C4×C5×C7×C25 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8875 |
| abelian | C71×C125 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C25 | C5×C71 |
| socle | C5×C71 | C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
8875 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic8875, C2×D8875 |
| maximal subgroup of | C2×C71×C125, C3×C71×C125, D8875 |
| maximal normal subgroup of | C2×C71×C125, C3×C71×C125, D8875 |
| maximal quotient of | C2×C71×C125, C3×C71×C125 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8875, 1);