Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D19×#87705 |
| Fitting, socle, derived, Hall | C7×C192 ⋊ C2×C3 |
| Hall | C19×#87705 ⋊ C2 |
| Hall | C7×C19×D19 ⋊ C3 |
| Hall | C19×D19 ⋊ ΓL(1,𝔽8) |
| Sylow | C192 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ D19×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C192 | C2×C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
517 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×#11716328, D19×#11716326, D19×#11716322, … |
| maximal normal subgroup of | D19×#11716328, D19×#11716326, D19×#11716322, … |
| maximal quotient of | Dic19×#87705, C2×D19×#87705 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 68);