Finite Group DatabasebetaFinite Group Databasebeta| order | 16129 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C7×C9×C127 (order 16002) · Inn(G) = C1 · Out(G) = C2×C7×C9×C127 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C16129 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, socle, prime radical, cosocle | C127 | C127 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C127 ▷ C1 | |
3 conjugacy classes of subgroups.
16129 conjugacy classes. The character table is too large to display.
| derived subgroup of | D16129, Dic16129, C2×D16129 |
| Fitting subgroup of | D16129 |
| maximal subgroup of | D16129, C2×C16129 |
| maximal normal subgroup of | D16129, C2×C16129 |
| maximal quotient of | C2×C16129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16129, 1);