Finite Group DatabasebetaFinite Group Databasebeta| order | 3940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C197 ⋊ C4 |
| Sylow | C197 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #11716161 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C197 | C4 |
| prime radical, cosocle | D985 | C2 |
| LCS | G ▷ C5×C197 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 202 |
| transitive degree | μt(G) = 985 |
Polycyclic presentation:
2^2,5,197|a^2=b,c^a=c^2,d^a=d^14,c^b=c^4,d^b=d^196250 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16841100, C3⋊#16841100, #34089221, … |
| maximal normal subgroup of | C3×#16841100, C5×#16841100, #16841100⋊C7, … |
| maximal quotient of | C3×#16841100, C3⋊#16841100, #34089221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3940, 9);