Finite Group DatabasebetaFinite Group Databasebeta| order | 8123 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C31×C131 (order 8122) · Inn(G) = C1 · Out(G) = C2×C31×C131 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8123 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
2 conjugacy classes of subgroups.
8123 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic8123, C2×D8123 |
| maximal subgroup of | D8123, C2×C8123, C3×C8123 |
| maximal normal subgroup of | D8123, C2×C8123, C3×C8123 |
| maximal quotient of | C2×C8123, C3×C8123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8123, 1);