Finite Group DatabasebetaFinite Group Databasebeta| order | 38598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D919⋊C3 |
| unambiguous semidirect product | D919⋊(C3×C7) |
| unambiguous semidirect product | (C919⋊C3)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C919 ⋊ C2×C3 |
| derived, Sylow | C919 ⋊ C2×C3×C7 |
| Hall | C7×C919⋊C3 ⋊ C2 |
| Hall | C7×D919 ⋊ C3 |
| Hall | C919⋊C3 ⋊ C2×C7 |
| Hall | D919 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D919⋊C3 |
| commutator, cosocle, hypocenter | C919 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C919 | C2×C3 |
| LCS | G ▷ C919 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6433 |
1113 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38598, 13);