Finite Group DatabasebetaFinite Group Databasebeta| order | 22914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C67 ⋊ C2×C9 |
| Hall | #26039286 ⋊ C2 |
| Hall | C19×D67 ⋊ C9 |
| Hall | D67 ⋊ #4296 |
| Sylow | C67 ⋊ C2×#4296 |
| Sylow | C19 ⋊ D67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C67 | C2×C9 |
| prime radical | C19⋊C3×D67 | C3 |
| cosocle | C19⋊C3×C67 | C2×C3 |
| LCS | G ▷ C19×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1273 |
Polycyclic presentation:
2,3^2,19,67|b^3=c,e^a=e^66,d^b=d^4,e^b=e^37,d^c=d^7121 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22914, 33);