Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C19 ⋊ C2×C3 |
| Hall | #23751432 ⋊ C2 |
| Hall | C13×C19×D13 ⋊ C3 |
| Hall | C13×D13 ⋊ C19⋊C3 |
| Sylow | C132 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ #11759817 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C19 | C2×C3 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 494 |
Polycyclic presentation:
2,3,13^2,19|c^a=c^12,c^b=c^3,d^b=d^3,e^b=e^7664 conjugacy classes — view the full character table.
| maximal subgroup of | #50310355, #50310360, #50310361, … |
| maximal normal subgroup of | #50310355, #50310360, #50310361, … |
| maximal quotient of | #50310221, C2×#34064216 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 51);