Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13×C19 ⋊ C2×C3 |
| Hall | #19104443 ⋊ C2 |
| Hall | D1729 ⋊ C3 |
| Hall | C13×C19 ⋊ AGL(1,𝔽7) |
| Hall | C7×C19 ⋊ D13⋊C3 |
| Hall | C7×C13 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ #10587723 |
| Sylow | C13 ⋊ #11716327 |
| Sylow | C7 ⋊ #13093367 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C19 | C2×C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,13,19|c^a=c^6,d^a=d^12,e^a=e^18,c^b=c^2,d^b=d^9,e^b=e^7294 conjugacy classes — view the full character table.
| maximal subgroup of | #35208924, #35208940, #35208942, … |
| maximal normal subgroup of | #35208924, #35208940, #35208942, … |
| maximal quotient of | #35208891, C2×#23780628, #44527636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 119);