Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#11716326 |
| Fitting, socle, Hall | C7×C192 ⋊ C2×C3 |
| derived | C7×C19 ⋊ C2×C3×C19 |
| Hall | C19×#87705 ⋊ C2 |
| Hall | D7×C192 ⋊ C3 |
| Sylow | C192 ⋊ AGL(1,𝔽7) |
| Hall | D7 ⋊ C19×C19⋊C3 |
| Sylow | C7 ⋊ C2×C19×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #11716326 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C192 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C19 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 399 |
703 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#11716322⋊C2, #11716326⋊D19, D19×#11716326, … |
| maximal normal subgroup of | C19×#11716322⋊C2, #11716326⋊D19, D19×#11716326, … |
| maximal quotient of | C19×#13097587, C2×C19×#11716326 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 38);