Finite Group DatabasebetaFinite Group Databasebeta| order | 19158 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#23751016 |
| Fitting, socle, Hall | C2×C31×C103 ⋊ C3 |
| derived, Hall | C31×C103 ⋊ C2×C3 |
| Hall | C2×C103 ⋊ C31⋊C3 |
| Sylow | C103 ⋊ C2×C31⋊C3 |
| Hall | C2×C31 ⋊ C103⋊C3 |
| Sylow | C31 ⋊ C2×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #23751016 |
| commutator, cosocle, hypocenter | C31×C103 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C103 | C3 |
| LCS | G ▷ C31×C103 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6386 |
2134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#23751016, #50305147, #50305151, … |
| maximal normal subgroup of | C4×#23751016, #50305147, #50305151, … |
| maximal quotient of | C4×#23751016, C22×#23751016 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19158, 5);