Finite Group DatabasebetaFinite Group Databasebeta| order | 13861 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C41×C83 (order 13612) · Inn(G) = C1 · Out(G) = C22×C41×C83 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C13861 |
| abelian | C83×C167 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4 conjugacy classes of subgroups.
13861 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic13861, C2×D13861 |
| maximal subgroup of | D83×C167, C83×D167, D13861, … |
| maximal normal subgroup of | D83×C167, C83×D167, D13861, … |
| maximal quotient of | C2×C83×C167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13861, 2);