Finite Group DatabasebetaFinite Group Databasebeta| order | 8171 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C5×C19×C43 (order 8170) · Inn(G) = C1 · Out(G) = C2×C5×C19×C43 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8171 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
2 conjugacy classes of subgroups.
8171 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic8171, C2×D8171 |
| maximal subgroup of | D8171, C2×C8171, C3×C8171 |
| maximal normal subgroup of | D8171, C2×C8171, C3×C8171 |
| maximal quotient of | C2×C8171, C3×C8171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8171, 1);