Finite Group DatabasebetaFinite Group Databasebeta| order | 15931 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C8×C11×C89 (order 15664) · Inn(G) = C1 · Out(G) = C2×C8×C11×C89 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C15931 |
| abelian | C89×C179 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4 conjugacy classes of subgroups.
15931 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic15931, C2×D15931 |
| maximal subgroup of | D89×C179, C89×D179, D15931, … |
| maximal normal subgroup of | D89×C179, C89×D179, D15931, … |
| maximal quotient of | C2×C89×C179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15931, 2);