Finite Group DatabasebetaFinite Group Databasebeta| order | 8138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D313⋊C13 |
| unambiguous semidirect product | (C313⋊C13)⋊C2 |
| Fitting, socle, derived, Sylow | C313 ⋊ C2×C13 |
| Hall | C313⋊C13 ⋊ C2 |
| Hall | D313 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C313 | C2×C13 |
| LCS | G ▷ C313 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,313|c^a=c^312,c^b=c^10338 conjugacy classes — view the full character table.
| maximal subgroup of | #11929411⋊C13, C2×D313⋊C13, C3×D313⋊C13, … |
| maximal normal subgroup of | #11929411⋊C13, C2×D313⋊C13, C3×D313⋊C13, … |
| maximal quotient of | Dic313⋊C13, C2×D313⋊C13, C3×D313⋊C13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8138, 1);