Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| isoclinism | isoclinic class of #87705 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C2×C19×#87705 |
| Fitting, socle, Hall | C2×C7×C192 ⋊ C3 |
| derived | C7×C19 ⋊ C2×C3×C19 |
| Hall | C7×C192 ⋊ C2×C3 |
| Hall | C2×C192 ⋊ ΓL(1,𝔽8) |
| Sylow | C192 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C19×C19⋊C3 |
| Sylow | C7 ⋊ C2×C19×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | #87705 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C192 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C2×C19 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
1786 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#13097589, C19×#13097587, #44476505, … |
| maximal normal subgroup of | C19×#13097589, C19×#13097587, #44476505, … |
| maximal quotient of | C4×C19×#87705, C22×C19×#87705 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 84);