Finite Group DatabasebetaFinite Group Databasebeta| order | 8638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C617⋊C7 |
| unambiguous semidirect product | (C2×C617)⋊C7 |
| Fitting, socle, Hall | C2×C617 ⋊ C7 |
| derived, Sylow | C617 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C617⋊C7 |
| commutator, hypocenter | C617 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C617 | C7 |
| LCS | G ▷ C617 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
190 conjugacy classes — view the full character table.
| maximal subgroup of | Dic617⋊C7, C4×C617⋊C7, C2×D617⋊C7, … |
| maximal normal subgroup of | Dic617⋊C7, C4×C617⋊C7, C2×D617⋊C7, … |
| maximal quotient of | C4×C617⋊C7, C22×C617⋊C7, C2×C3×C617⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8638, 2);