Finite Group DatabasebetaFinite Group Databasebeta| order | 8638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D617⋊C7 |
| unambiguous semidirect product | (C617⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C617 ⋊ C2×C7 |
| Hall | C617⋊C7 ⋊ C2 |
| Hall | D617 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C617 | C2×C7 |
| LCS | G ▷ C617 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,617|c^a=c^616,c^b=c^42058 conjugacy classes — view the full character table.
| maximal subgroup of | #14578674⋊C7, C2×D617⋊C7, C3×D617⋊C7, … |
| maximal normal subgroup of | #14578674⋊C7, C2×D617⋊C7, C3×D617⋊C7 |
| maximal quotient of | Dic617⋊C7, C2×D617⋊C7, C3×D617⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8638, 1);