Finite Group DatabasebetaFinite Group Databasebeta| order | 15879 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×C67⋊C3 |
| unambiguous semidirect product | C67⋊(C3×C79) |
| Fitting, socle, Hall | C67×C79 ⋊ C3 |
| derived, Sylow | C67 ⋊ C3×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C3×C79 |
| Frattini | C1 | G |
| Fitting, socle | C67×C79 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C79 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5293 |
1975 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C79×C67⋊C3, D79×C67⋊C3, C79×D67⋊C3, … |
| maximal normal subgroup of | C2×C79×C67⋊C3, D79×C67⋊C3, C79×D67⋊C3, … |
| maximal quotient of | C2×C79×C67⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15879, 1);