Finite Group DatabasebetaFinite Group Databasebeta| order | 4503 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C79 ⋊ C3 |
| Sylow | C79 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C79 | C3 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 1501 |
Polycyclic presentation:
3,19,79|b^a=b^7,c^a=c^23503 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×C79⋊C3, C3×#17985163, C22⋊#17985163, … |
| maximal normal subgroup of | C19⋊C3×C79⋊C3, C3×#17985163, C5×#17985163, … |
| maximal quotient of | #27214005, C3×#17985163, C22⋊#17985163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4503, 3);