Finite Group DatabasebetaFinite Group Databasebeta| order | 3598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D257 |
| unambiguous semidirect product | C257⋊(C2×C7) |
| Fitting, socle, Hall | C7×C257 ⋊ C2 |
| derived, Sylow | C257 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D257 |
| commutator, cosocle, hypocenter | C257 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C257 | C2 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 264 |
| transitive degree | μt(G) = 1799 |
910 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D257, C7×D1285, C49×D257, … |
| maximal normal subgroup of | C5×C7×D257, C49×D257, C72×D257 |
| maximal quotient of | C5×C7×D257, C7×D1285, C49×D257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3598, 2);