Finite Group DatabasebetaFinite Group Databasebeta| order | 6740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C337 ⋊ C4 |
| Sylow | C337 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #13062438 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C337 | C4 |
| LCS | G ▷ C5×C337 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,337|a^2=b,c^a=c^2,d^a=d^148,c^b=c^4,d^b=d^336425 conjugacy classes — view the full character table.
| maximal subgroup of | #20269798⋊C3, C3×#20269798, C3⋊#20269798, … |
| maximal normal subgroup of | #20269798⋊C3, C3×#20269798, C5×#20269798 |
| maximal quotient of | C3×#20269798, C3⋊#20269798, #46797754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6740, 8);