Finite Group DatabasebetaFinite Group Databasebeta| order | 15010 |
| isoclinism | isoclinic class of D79 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×D79 |
| unambiguous semidirect product | C79⋊(C2×C5×C19) |
| Fitting, socle, Hall | C5×C19×C79 ⋊ C2 |
| derived, Sylow | C79 ⋊ C2×C5×C19 |
| Hall | C19×C79 ⋊ C2×C5 |
| Hall | C5×C79 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | D79 |
| commutator, cosocle, hypocenter | C79 | C2×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C79 | C2 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C5×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7505 |
3895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D19×D79, D5×C19×D79, D79×D95, … |
| maximal normal subgroup of | C5×D19×D79, D5×C19×D79, D79×D95, … |
| maximal quotient of | C5×C19×Dic79, C2×C5×C19×D79 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15010, 2);