Finite Group DatabasebetaFinite Group Databasebeta| order | 14319 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C43 ⋊ C9 |
| Sylow | C43 ⋊ #66526 |
| Sylow | C37 ⋊ C43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C43 | C9 |
| prime radical, cosocle | C43×C37⋊C3 | C3 |
| LCS | G ▷ C37×C43 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1591 |
Polycyclic presentation:
3^2,37,43|a^3=b,c^a=c^16,d^a=d^6,c^b=c^26223 conjugacy classes — view the full character table.
| maximal subgroup of | #43270519, #43270521, #43270524, … |
| maximal normal subgroup of | #43270519, #43270521, #43270524, … |
| maximal quotient of | C2×#28384891 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14319, 9);